# migrations

dir: embeddings_queue
filename: 00001-embeddings.sqlite.sql
hash: d3755dfd232be8e8301f4d7fcfb3a486
sql:
CREATE TABLE embeddings_queue (
    seq_id INTEGER PRIMARY KEY,
    created_at TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP,
    operation INTEGER NOT NULL,
    topic TEXT NOT NULL,
    id TEXT NOT NULL,
    vector BLOB,
    encoding TEXT,
    metadata TEXT
);


dir: sysdb
filename: 00001-collections.sqlite.sql
hash: 38352d725ad1c16074fac420b22b4633
sql:
CREATE TABLE collections (
    id TEXT PRIMARY KEY,
    name TEXT NOT NULL,
    topic TEXT NOT NULL,
    UNIQUE (name)
);

CREATE TABLE collection_metadata (
    collection_id TEXT REFERENCES collections(id) ON DELETE CASCADE,
    key TEXT NOT NULL,
    str_value TEXT,
    int_value INTEGER,
    float_value REAL,
    PRIMARY KEY (collection_id, key)
);


dir: sysdb
filename: 00002-segments.sqlite.sql
hash: 2913cb6a503055a95f625448037e8912
sql:
CREATE TABLE segments (
    id TEXT PRIMARY KEY,
    type TEXT NOT NULL,
    scope TEXT NOT NULL,
    topic TEXT,
    collection TEXT REFERENCES collection(id)
);

CREATE TABLE segment_metadata (
    segment_id TEXT  REFERENCES segments(id) ON DELETE CASCADE,
    key TEXT NOT NULL,
    str_value TEXT,
    int_value INTEGER,
    float_value REAL,
    PRIMARY KEY (segment_id, key)
);


dir: sysdb
filename: 00004-tenants-databases.sqlite.sql
hash: 048867ce8fcdefe4023c7110e4433591
sql:
CREATE TABLE IF NOT EXISTS tenants (
    id TEXT PRIMARY KEY,
    UNIQUE (id)
);

CREATE TABLE IF NOT EXISTS databases (
    id TEXT PRIMARY KEY, -- unique globally
    name TEXT NOT NULL, -- unique per tenant
    tenant_id TEXT NOT NULL REFERENCES tenants(id) ON DELETE CASCADE,
    UNIQUE (tenant_id, name) -- Ensure that a tenant has only one database with a given name
);

CREATE TABLE IF NOT EXISTS collections_tmp (
    id TEXT PRIMARY KEY, -- unique globally
    name TEXT NOT NULL, -- unique per database
    topic TEXT NOT NULL,
    dimension INTEGER,
    database_id TEXT NOT NULL REFERENCES databases(id) ON DELETE CASCADE,
    UNIQUE (name, database_id)
);

-- Create default tenant and database
INSERT OR REPLACE INTO tenants (id) VALUES ('default_tenant'); -- The default tenant id is 'default_tenant' others are UUIDs
INSERT OR REPLACE INTO databases (id, name, tenant_id) VALUES ('00000000-0000-0000-0000-000000000000', 'default_database', 'default_tenant');

INSERT OR REPLACE INTO collections_tmp (id, name, topic, dimension, database_id)
    SELECT id, name, topic, dimension, '00000000-0000-0000-0000-000000000000' FROM collections;
DROP TABLE collections;
ALTER TABLE collections_tmp RENAME TO collections;


dir: sysdb
filename: 00005-remove-topic.sqlite.sql
hash: b1367c826b8fba5f96f27befdc1d42d2
sql:
-- Remove the topic column from the Collections and Segments tables

ALTER TABLE collections DROP COLUMN topic;
ALTER TABLE segments DROP COLUMN topic;


dir: metadb
filename: 00001-embedding-metadata.sqlite.sql
hash: 2b4cf52c4bb2676e21d6860a4409f856
sql:
CREATE TABLE embeddings (
    id INTEGER PRIMARY KEY,
    segment_id TEXT NOT NULL,
    embedding_id TEXT NOT NULL,
    seq_id BLOB NOT NULL,
    created_at TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP,
    UNIQUE (segment_id, embedding_id)
);

CREATE TABLE embedding_metadata (
    id INTEGER REFERENCES embeddings(id),
    key TEXT NOT NULL,
    string_value TEXT,
    int_value INTEGER,
    float_value REAL,
    PRIMARY KEY (id, key)
);

CREATE TABLE max_seq_id (
    segment_id TEXT PRIMARY KEY,
    seq_id BLOB NOT NULL
);

CREATE VIRTUAL TABLE embedding_fulltext USING fts5(id, string_value);


dir: metadb
filename: 00002-embedding-metadata.sqlite.sql
hash: 12a570f7121b3a8ce750a2a7c36da20f
sql:
-- SQLite does not support adding check with alter table, as a result, adding a check
-- involve creating a new table and copying the data over. It is over kill with adding
-- a boolean type column. The application write to the table needs to ensure the data
-- integrity.
ALTER TABLE embedding_metadata ADD COLUMN bool_value INTEGER


dir: metadb
filename: 00003-full-text-tokenize.sqlite.sql
hash: f97ad6334aeaa8f419f01110b648b97a
sql:
CREATE VIRTUAL TABLE embedding_fulltext_search USING fts5(string_value, tokenize='trigram');
INSERT INTO embedding_fulltext_search (rowid, string_value) SELECT rowid, string_value FROM embedding_metadata;
DROP TABLE embedding_fulltext;


dir: sysdb
filename: 00006-collection-segment-metadata.sqlite.sql
hash: 4eea7468935bf25d4604a0fed2366116
sql:
-- SQLite does not support adding check with alter table, as a result, adding a check
-- involve creating a new table and copying the data over. It is over kill with adding
-- a boolean type column. The application write to the table needs to ensure the data
-- integrity.
ALTER TABLE collection_metadata ADD COLUMN bool_value INTEGER;
ALTER TABLE segment_metadata ADD COLUMN bool_value INTEGER;


dir: sysdb
filename: 00007-collection-config.sqlite.sql
hash: 1c7e63bba346a42a18b6ab7f1c989bed
sql:
-- Stores collection configuration dictionaries.
ALTER TABLE collections ADD COLUMN config_json_str TEXT;


# embeddings_queue

created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 9696b597-b6a3-4033-8529-c38ed13ee015
encoding: FLOAT32
metadata:
{"key": "1", "chroma:document": "Mrs. Watson wants to invest in the real-estate market and has a total budget of at most TotalBudget. She has two choices which include condos and detached houses. Each dollar invested in condos yields a ProfitPerDollarCondos profit and each dollar invested in detached houses yields a ProfitPerDollarHouses profit. A minimum of MinPercentageCondos of the total investment must be in condos, and at least MinInvestmentDetached must be invested in detached houses."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 3139b68d-569f-4860-9417-2e3e591ec076
encoding: FLOAT32
metadata:
{"key": "2", "chroma:document": "A breakfast joint makes two different sandwiches: a regular and a special. Both need eggs and bacon. Each regular sandwich requires EggsPerRegular eggs and BaconPerRegular slices of bacon. Each special sandwich requires EggsPerSpecial eggs and BaconPerSpecial slices of bacon. The joint has a total of TotalEggs eggs and TotalBacon slices of bacon. It makes a profit of ProfitRegular per regular sandwich and a profit of ProfitSpecial per special sandwich. How many of each sandwich should be made to maximize profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 1945dbab-5b7e-402d-ab5d-a3583e5ba8b0
encoding: FLOAT32
metadata:
{"key": "3", "chroma:document": "A cleaning company aims to maximize exposure for promoting their new product without exceeding their TotalBudget. They will advertise using radio ads and social media ads. Each radio ad costs CostRadioAd and provides ExposureRadioAd exposure. Each social media ad costs CostSocialMediaAd and delivers ExposureSocialMediaAd exposure. The company aims to run between MinRadioAds and MaxRadioAds radio ads and at least MinSocialMediaAds social media ads while staying within the TotalBudget."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 9ea7ed9f-2260-49bd-8907-4365cafc7b6a
encoding: FLOAT32
metadata:
{"key": "4", "chroma:document": "There is TotalGold available that is needed to make long and short cables. Long cables require GoldPerLongCable while short cables require GoldPerShortCable. Because of their compact size, the number of short cables should be at least ShortCableMultiplier times the number of long cables. In addition, there needs to be at least MinLongCables made. If each long cable sold results in a ProfitPerLongCable and each short cable sold results in a ProfitPerShortCable, how many of each type of cable should be made to maximize profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 5a5fb9f8-b2d2-482c-b904-030684dbfa71
encoding: FLOAT32
metadata:
{"key": "6", "chroma:document": "A company is deciding where to promote their product across NumMedia types of media. Each medium has a cost and a number of viewers it attracts per advertisement, defined by CostMedia and ViewersMedia respectively. SzoorchleEngine has a maximum number of advertisements constraint, MaxSzoorchleAds. To balance advertising, at most MaxWassaProportion of the total number of ads should be on Wassa, and at least MinZTubeProportion of the total number of ads should be on ZTube. The total weekly advertising budget is defined by Budget. The goal is to determine the number of advertisements on each type of media to maximize the total audience while adhering to these constraints."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 7e1e7a8d-8bf4-49fd-b2fe-5563afd9f94c
encoding: FLOAT32
metadata:
{"key": "7", "chroma:document": "A furniture company produces two types of products, chairs and dressers. The profit from each chair is ChairProfit, while the profit from each dresser is DresserProfit. Every week, the company has TotalStain gallons of stain and TotalOakWood lengths of oak wood available. Each chair requires StainPerChair gallons of stain and WoodPerChair lengths of oak wood, while each dresser requires StainPerDresser gallons of stain and WoodPerDresser lengths of oak wood. The goal is to determine the number of chairs and dressers to produce in order to maximize the total profit, given the constraints on the availability of stain and oak wood."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 82735154-9e44-4e8f-89c3-ac05b0d7254d
encoding: FLOAT32
metadata:
{"key": "8", "chroma:document": "A farmer wants to mix his animal feeds, Feed A and Feed B, in such a way that the mixture will contain a minimum of MinProtein units of protein and MinFat units of fat. Feed A costs CostFeedA per kilogram and contains ProteinFeedA units of protein and FatFeedA units of fat. Feed B costs CostFeedB per kilogram and contains ProteinFeedB units of protein and FatFeedB units of fat. Determine the minimum cost of the mixture."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: b7487263-a097-4666-a1ef-cd0ac3f64a44
encoding: FLOAT32
metadata:
{"key": "9", "chroma:document": "An artisan makes two types of terracotta jars: a thin jar and a stubby jar. Each thin jar requires ShapingTimeThinJar minutes of shaping time and BakingTimeThinJar minutes of baking time. Each stubby jar requires ShapingTimeStubbyJar minutes of shaping time and BakingTimeStubbyJar minutes of baking time. Per week, there are TotalShapingTime minutes available for shaping and TotalBakingTime minutes available for baking. The profit per thin jar is ProfitThinJar and the profit per stubby jar is ProfitStubbyJar. How many jars of each type should the artisan make to maximize profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: ce8c61f4-d743-4899-8522-8833c36b5bd5
encoding: FLOAT32
metadata:
{"key": "10", "chroma:document": "A grocery store wants to liquidate its stock of TotalApples apples, TotalBananas bananas, and TotalGrapes grapes. Given past experience, the store knows that they can propose a banana-haters package with ApplesInBananaHaters apples and GrapesInBananaHaters grapes, and that this package will bring a profit of ProfitBananaHaters euros. Similarly, they can prepare a combo package with ApplesInCombo apples, BananasInCombo bananas, and GrapesInCombo grapes, yielding a profit of ProfitCombo euros. They know they can sell any quantity of these two packages within the availability of its stock. What quantity of each package, banana-haters packages and combo packages, should the store prepare to maximize net profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 2b0758ac-6b29-46e2-9b39-fc155501448f
encoding: FLOAT32
metadata:
{"key": "11", "chroma:document": "A bakery uses a stand-mixer and a slow bake oven to make products. Each machine can run for at most MaxHours per year. To produce one unit of bread takes BreadMixerTime time in the stand mixer and BreadOvenTime time in the oven. A unit of cookies requires CookieMixerTime time in the mixer and CookieOvenTime time in the oven. The profit per unit of bread is ProfitBread and the profit per unit of cookies is ProfitCookie. How should the bakery operate to maximize total profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 8424cec5-7adc-4d4f-8367-0fd7c5a7a083
encoding: FLOAT32
metadata:
{"key": "12", "chroma:document": "A factory makes two types of glass panes: a regular glass pane and a tempered glass pane. Both require time on a heating and cooling machine. Both machines are available for a maximum of MaxHeatingTime minutes per day for the heating machine and MaxCoolingTime minutes per day for the cooling machine. It takes HeatingTimeRegular minutes in the heating machine and CoolingTimeRegular minutes in the cooling machine to make one regular glass pane. It takes HeatingTimeTempered minutes in the heating machine and CoolingTimeTempered minutes in the cooling machine to make one tempered glass pane. The profit per pane of regular glass is ProfitRegular and the profit per pane of tempered glass is ProfitTempered. How many panes of each glass type should the factory make to maximize profit? What is the maximum profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: debc6f87-0c31-445d-8076-28dc7483824c
encoding: FLOAT32
metadata:
{"key": "13", "chroma:document": "A shop makes two types of souvenirs, Elephants and Tigers. Each Elephant requires WoodPerElephant amount of wood and PlasticPerElephant amount of plastic. Each Tiger requires WoodPerTiger amount of wood and PlasticPerTiger amount of plastic. The shop has TotalWoodAvailable amount of wood and TotalPlasticAvailable amount of plastic available each week. The profit from selling one Elephant is ProfitPerElephant, and the profit from selling one Tiger is ProfitPerTiger. Determine the number of Elephants and Tigers to make to maximize the total profit."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: b02ffec1-1afb-428b-b39d-1200075a75ab
encoding: FLOAT32
metadata:
{"key": "15", "chroma:document": "The family has TotalInvest amount of money to invest, with some in apartments and the rest in townhouses. The amount of money invested in apartments must not exceed MaxInvestApt. The investment in apartments must be at least a MinRatioInvestAptToTown times the investment in townhouses. The return rate for investment in apartments is ReturnRateApt, and the return rate for investment in townhouses is ReturnRateTown. The goal is to determine the optimal investment in apartments and townhouses to maximize profit."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 01e34d56-3321-4659-8e06-f6648a9cc6b5
encoding: FLOAT32
metadata:
{"key": "16", "chroma:document": "An individual needs to take at least MinZ1 grams of Z1 and MinD3 grams of D3 daily. These medicines are available in two types of pills: Zodiac and Sunny. One pill of Zodiac contains Z1InZodiac grams of Z1 and D3InZodiac grams of D3. One pill of Sunny contains Z1InSunny grams of Z1 and D3InSunny grams of D3. The cost per pill of Zodiac is CostZodiac, and the cost per pill of Sunny is CostSunny. The objective is to determine the quantity of Zodiac and Sunny pills that should be taken to meet the medicine requirements at the lowest cost."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: f9dff671-7ddf-48e4-b03d-74a2be94dc75
encoding: FLOAT32
metadata:
{"key": "17", "chroma:document": "A hobbyist makes model trains and planes using TotalWood and TotalPaint. A model train requires WoodPerTrain units of wood and PaintPerTrain units of paint. A model plane requires WoodPerPlane units of wood and PaintPerPlane units of paint. The hobbyist has available TotalWood units of wood and TotalPaint units of paint. If the profit per model train is ProfitPerTrain and the profit per model plane is ProfitPerPlane, how many of each should be made to maximize his profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: e20ae008-b957-43cb-9b7d-45eb3f4a798a
encoding: FLOAT32
metadata:
{"key": "18", "chroma:document": "A store wants to maximize its profit by optimizing the inventory of phones and laptops. The profit earned per phone is ProfitPhone, and the profit earned per laptop is ProfitLaptop. Each phone requires SpacePhone floor space, and each laptop requires SpaceLaptop floor space, with a total available floor space given by TotalSpace. Corporate policy mandates that at least MinLaptopPercentage of all items in the inventory be laptops. The cost for the store to purchase each phone is CostPhone, and each laptop costs CostLaptop. The store aims to keep the total spending within MaxSpending."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 00f22ede-9701-41eb-8ce6-179ad1a2ccec
encoding: FLOAT32
metadata:
{"key": "19", "chroma:document": "A candy store mixes different types of candy to prepare two types of products: regular mix and sour surprise mix. Each kilogram of the regular mix contains RegularCandyInRegularMix kilograms of regular candy and SourCandyInRegularMix kilograms of sour candy. The profit per kilogram of the regular mix is ProfitRegularMix. Each kilogram of the sour surprise mix contains RegularCandyInSourMix kilograms of regular candy and SourCandyInSourMix kilograms of sour candy. The profit per kilogram of the sour surprise mix is ProfitSourMix. The candy store has AvailableRegularCandy kilograms of regular candy and AvailableSourCandy kilograms of sour candy available. The goal is to determine how many kilograms of each type of product should be created to maximize the total profit given the available candy."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: f439491c-5305-48a8-84d9-da7702531aa1
encoding: FLOAT32
metadata:
{"key": "20", "chroma:document": "A factory has TotalSpace of space to allocate between the production of phones and laptops, where each type of product occupies a certain amount of space per unit of production. Phones require PhoneLabor hours of labor and cost PhoneCost per square foot of space allocated for phone production. Laptops require LaptopLabor hours of labor and cost LaptopCost per square foot of space allocated for laptop production. Phones produce a net revenue of PhoneRevenue per square foot while laptops produce a net revenue of LaptopRevenue per square foot. The factory aims to spend at most TotalBudget and use at most TotalLabor hours of labor. The goal is to determine the optimal allocation of TotalSpace between phones and laptops to maximize total net revenue."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: d077b17c-ee69-48a1-b3b1-606f136af910
encoding: FLOAT32
metadata:
{"key": "21", "chroma:document": "An electronics store sells premium desktops with more power as well as regular desktops for everyday use. Each premium desktop costs the store CostPremium to make and yields a profit of ProfitPremium. Each regular desktop costs the store CostRegular to make and yields a profit of ProfitRegular. The store sells at most MaxDesktops desktops each month and wants to spend at most MaxBudget on making the desktops. How many of each should be made and sold to maximize profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 32f32654-effe-41e8-a4d8-924e62034997
encoding: FLOAT32
metadata:
{"key": "22", "chroma:document": "A car manufacturer makes two versions of the same car, a regular model and a premium model. They make x1 regular models per day and x2 premium models per day. The profit per regular model is ProfitRegular and the profit per premium model is ProfitPremium (x1 and x2 are unknown values both greater than or equal to 0). The daily demand for these cars is limited to at most MaxDemandRegular regular models and MaxDemandPremium premium models. In addition, the manufacturer can make a maximum of MaxTotalProduction cars of either type per day. How many cars of each model should the manufacturer make in order to maximize profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: b280c675-725d-436e-a674-9c4b5d0e53db
encoding: FLOAT32
metadata:
{"key": "23", "chroma:document": "You are designing an office space with two types of desks: long desks and short desks. You can spend at most Budget. Long desks cost CostLongDesk, take up SpaceLongDesk of space, and seat SeatingLongDesk employees. Short desks cost CostShortDesk, take up SpaceShortDesk of space, and seat SeatingShortDesk employees. The office can have at most MaxSpace of desks. How many of each desk should you buy in order to maximize the seating availability?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: fdcd2ea9-c6b4-460a-af59-5913b74f9f04
encoding: FLOAT32
metadata:
{"key": "24", "chroma:document": "Ayse produces a plant growth compound by mixing two types of fertilizer: C and Y. This growth compound must contain at least MinRequiredNitrousOxide units of nitrous oxide and MinRequiredVitaminMix units of vitamin mix. Fertilizer C and Y cost CostPerKgFertilizerC and CostPerKgFertilizerY per kg respectively. Fertilizer C contains NitrousOxidePerKgC units of nitrous oxide per kg and VitaminMixPerKgC units of vitamin mix per kg. Fertilizer Y contains NitrousOxidePerKgY units of nitrous oxide per kg and VitaminMixPerKgY units of vitamin mix per kg. Determine the minimum cost of Ayse's compound."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 0ecdce27-959b-47ca-af2a-6b44e63dd8bd
encoding: FLOAT32
metadata:
{"key": "26", "chroma:document": "A car manufacturer makes NumOilTypes types of car oils. A container of each oil type contains different amounts of NumSubstances substances. The car manufacturer has a certain total amount of each substance available. Additionally, the profit per container of each oil type is given. The manufacturer wants to determine how many containers of each oil type should be made to maximize profit."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 13aab5b4-1b7d-416b-821e-be6899aa59b8
encoding: FLOAT32
metadata:
{"key": "27", "chroma:document": "A food truck owner can spend at most TotalBudget on purchasing mangos and guavas. A mango costs MangoCost and a guava costs GuavaCost. Each mango is sold for a profit of MangoProfit while each guava is sold for a profit of GuavaProfit. The owner estimates that at least MinMangosSold but at most MaxMangosSold mangos are sold each month. He also estimates that the number of guavas sold is at most MaxGuavasPerMango of the mangos sold. The objective is to determine how many mangos and guavas should be sold to maximize the profit."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 7593882b-bf11-473d-8e69-3204b14a011e
encoding: FLOAT32
metadata:
{"key": "28", "chroma:document": "A nutritionist is making a special vitamin mix using two drinks: A and B. The vitamin mix must contain at least MinVitaminA units of Vitamin A, at least MinVitaminD units of Vitamin D, and at most MaxVitaminE units of Vitamin E. A cup of drink A contains VitaminAInA units of Vitamin A, VitaminDInA units of Vitamin D, VitaminEInA units of Vitamin E, and VitaminKInA units of Vitamin K. A cup of drink B contains VitaminAInB units of Vitamin A, VitaminDInB units of Vitamin D, VitaminEInB units of Vitamin E, and VitaminKInB units of Vitamin K. How many cups of each drink should be used to make the vitamin mix in order to minimize the amount of Vitamin K?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 0e0a0cba-1540-4cb7-8342-9c38639b311a
encoding: FLOAT32
metadata:
{"key": "29", "chroma:document": "An ice cream store makes two types of ice cream, chocolate and vanilla. In a week, they must produce at least MinChocolateGallons and at most MaxChocolateGallons of chocolate ice cream, and at least MinVanillaGallons and at most MaxVanillaGallons of vanilla ice cream. The time required to produce one gallon of chocolate ice cream is TimePerGallonChocolate hours, and the time required to produce one gallon of vanilla ice cream is TimePerGallonVanilla hours. The total available time for production in a week is TotalAvailableHours hours. Additionally, at least MinWorkers workers are needed at any time, with at least WorkersPerGallonChocolate workers working on chocolate ice cream and at least WorkersPerGallonVanilla workers working on vanilla ice cream. The profit per gallon of chocolate ice cream is ProfitPerGallonChocolate, and the profit per gallon of vanilla ice cream is ProfitPerGallonVanilla. The objective is to determine the number of gallons of each type of ice cream to produce in order to maximize profit."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: fd535b98-c901-458b-b247-110a2e77ccb9
encoding: FLOAT32
metadata:
{"key": "30", "chroma:document": "Mark has TotalLand acres of land available to grow potatoes and cucumbers that he sells at a farmers' market. He must grow at least MinPotatoes acres of potatoes and MinCucumbers acres of cucumbers to meet his contract. Mark prefers to grow more cucumbers than potatoes, but he only has enough resources to grow at most MaxCucumberToPotatoRatio times the amount of cucumbers as potatoes. If the profit per acre of potatoes is ProfitPerAcrePotato and the profit per acre of cucumbers is ProfitPerAcreCucumber, how many acres of each should he grow to maximize his profit? What is that profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: b8476904-11eb-4676-aa3e-f98206d01ff7
encoding: FLOAT32
metadata:
{"key": "31", "chroma:document": "A flooring company produces hardwood and vinyl planks. The demand for hardwood flooring each week is at least MinDemandHardwood square feet, and the demand for vinyl planks each week is at least MinDemandVinyl square feet. The total amount of flooring shipped each week must be at least MinTotalShipment square feet. Due to a labor shortage, the company can produce no more than MaxProductionHardwood square feet of hardwood flooring and no more than MaxProductionVinyl square feet of vinyl planks each week. The profit from producing a square foot of hardwood flooring is ProfitHardwood, while the profit from producing a square foot of vinyl planks is ProfitVinyl. The goal is to determine the number of square feet of each type of flooring to produce each week to maximize the company\u2019s profit."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: df7439c0-7b88-4d09-b8f2-4319af3c8858
encoding: FLOAT32
metadata:
{"key": "32", "chroma:document": "A farmer has two farms, where he grows NumBerryTypes different types of berries. He has a contract to provide specific quantities of each type of berry to a local store (DeliveryRequirement). It costs OldFarmCost to operate the old farm per day, where OldFarmOutput of each type of berry can be harvested and delivered in a day. It costs NewFarmCost to operate the new farm per day, where NewFarmOutput of each type of berry is harvested and delivered in a day. The goal is to meet the DeliveryRequirement for each type of berry while minimizing the total operation cost."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 921fe2c0-2de1-462d-ac0b-697d88f0e938
encoding: FLOAT32
metadata:
{"key": "33", "chroma:document": "Jordan wants to design a diet consisting of items Rice and Kebab. The cost per serving of Rice is represented by CostRice, and the cost per serving of Kebab is represented by CostKebab. Each serving of Rice provides CaloriesRice calories and ProteinRice grams of protein, while each serving of Kebab provides CaloriesKebab calories and ProteinKebab grams of protein. The goal is to minimize the total cost of the diet while ensuring that the total daily calorie intake is at least MinCalories calories and the total daily protein intake is at least MinProtein grams."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 1355a7b9-3e66-4ba7-b3b4-d6c31ff708ac
encoding: FLOAT32
metadata:
{"key": "34", "chroma:document": "A company sells custom scooters and bikes. The ProfitPerScooter and ProfitPerBike are given as abstract symbols. Each scooter requires DesignTimePerScooter with the design team and EngineeringTimePerScooter with the engineering team. Each bike requires DesignTimePerBike with the design team and EngineeringTimePerBike with the engineering team. Per month, there are TotalDesignHours available on the design team and TotalEngineeringHours available on the engineering team. Determine the monthly production quantities of scooters and bikes to maximize profit."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: d1ee74dd-e2dd-47ab-b491-b83cf0813677
encoding: FLOAT32
metadata:
{"key": "36", "chroma:document": "A person only eats two types of food: vegetables and fruits. Each serving of vegetables contains a certain amount of vitamins and minerals, and each serving of fruits contains a different amount of vitamins and minerals. The person wants to consume a minimum required amount of vitamins and minerals. The cost per serving of vegetables and fruits is specified. The goal is to determine the number of servings of vegetables and fruits to consume in order to meet the minimum vitamin and mineral requirements while minimizing the total cost."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 7886d4f9-3122-4839-b3ae-d14d1d5bdff8
encoding: FLOAT32
metadata:
{"key": "37", "chroma:document": "A bakery bakes two types of products: bagels and croissants. A batch of bagels requires OvenTimeBagels of oven time and ChefTimeBagels of pastry chef time. A batch of croissants requires OvenTimeCroissants of oven time and ChefTimeCroissants of pastry chef time. The bakery has a maximum of MaxOvenTime hours available for the oven and MaxChefTime hours available for the pastry chef each day. The profit per batch is ProfitBagels for bagels and ProfitCroissants for croissants. The objective is to maximize profit using the available capacity."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: b86b19ba-9062-4443-9a72-701ccec3f1e9
encoding: FLOAT32
metadata:
{"key": "38", "chroma:document": "A teddy bear company produces three different colored bears using two factories. Running the first factory for one hour costs CostFactory1 and produces ProductionBlackFactory1 black teddy bears, ProductionWhiteFactory1 white teddy bears, and ProductionBrownFactory1 brown teddy bears. Running the second factory for one hour costs CostFactory2 and produces ProductionBlackFactory2 black teddy bears and ProductionWhiteFactory2 white teddy bears but no brown teddy bears. The company needs to meet a daily demand of at least DemandBlack black teddy bears, DemandWhite white teddy bears, and DemandBrown brown teddy bears. The goal is to minimize the cost of production while fulfilling the demand."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 4df667ed-d76f-4466-8402-e2becea75dcc
encoding: FLOAT32
metadata:
{"key": "39", "chroma:document": "A farmer has TotalAcres acres of land to grow turnips and pumpkins. Turnips require WateringPerAcreTurnips minutes of watering and PesticidePerAcreTurnips worth of pesticide per acre. Pumpkins require WateringPerAcrePumpkins minutes of watering and PesticidePerAcrePumpkins worth of pesticide per acre. The farmer has TotalWateringTime minutes available for watering and TotalPesticideBudget available to spend on pesticide. If the revenue per acre of turnips is RevenuePerAcreTurnips and the revenue per acre of pumpkins is RevenuePerAcrePumpkins, how many acres of each should he grow to maximize his revenue."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: a04b8310-1d65-4788-9666-f093b45729f4
encoding: FLOAT32
metadata:
{"key": "40", "chroma:document": "A school employs staff and substitute teachers. Per shift, staff teachers work StaffHoursPerShift hours and get paid StaffWagePerShift. Per shift, substitute teachers work SubstituteHoursPerShift hours and get paid SubstituteWagePerShift. The school requires RequiredHours of teaching availability. If the school has a budget of TotalBudget, how many of each teacher should be hired to minimize the total number of teachers?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 9b7bdbd4-d550-4c63-998e-8006f4c35be1
encoding: FLOAT32
metadata:
{"key": "41", "chroma:document": "A factory uses HighIntensityDrills and LowIntensityDrills to process DailyGemProcessingRequirement gems each day. Each HighIntensityDrill has a capacity of HighIntensityDrillCapacity gems and requires HighIntensityDrillWaterRequirement units of water per day. Each LowIntensityDrill has a capacity of LowIntensityDrillCapacity gems and requires LowIntensityDrillWaterRequirement units of water per day. The total available water per day is TotalAvailableWater. At most MaxFractionHighIntensityDrills of the drills can be HighIntensityDrills, and at least MinLowIntensityDrills of the drills must be LowIntensityDrills. The goal is to determine the number of HighIntensityDrills and LowIntensityDrills required to minimize the total number of drills needed."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: d7aaf83f-ad3f-4aec-8004-0e367e7005c4
encoding: FLOAT32
metadata:
{"key": "42", "chroma:document": "A sandwich company can open two types of stores: dine-in places, each requiring EmployeesDineIn employees and producing ProductionDineIn sandwiches per day, and food-trucks, each requiring EmployeesFoodTruck employees and producing ProductionFoodTruck sandwiches per day. The company must produce at least MinProduction sandwiches per day and has TotalEmployees employees available. The objective is to determine how many of each type of store to open to minimize the total number of stores."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 2681b545-0df9-4bb6-afa2-9b2b2de83cc9
encoding: FLOAT32
metadata:
{"key": "43", "chroma:document": "There are two processes, process A and process B, to plate coins with gold. Process A requires GoldRequiredA units of gold, WiresRequiredA number of wires, and can plate CoinsPlatedA number of coins. Process B requires GoldRequiredB units of gold, WiresRequiredB number of wires, and can plate CoinsPlatedB number of coins. There are TotalGoldAvailable units of gold and TotalWiresAvailable number of wires available. How many processes of each type should be run to maximize the total number of coins that can be plated?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: f7c0dc31-4159-4cd4-99aa-a478f3587f80
encoding: FLOAT32
metadata:
{"key": "44", "chroma:document": "A woodshop can purchase two types of saws, a miter saw and a circular saw. A miter saw has a cutting capacity of MiterCutCapacity and produces MiterSawdust units of sawdust per day. A circular saw has a cutting capacity of CircularCutCapacity and produces CircularSawdust units of sawdust per day. The woodshop must cut at least MinPlanks planks of wood per day. However, to avoid too much pollution, they can produce at most MaxSawdust units of sawdust per day. The goal is to determine how many of each type of saw should be purchased to minimize the total number of saws needed."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: e0e6d7d6-a734-48c0-8cee-b4c9f403dec7
encoding: FLOAT32
metadata:
{"key": "45", "chroma:document": "A farmer has TotalAcres of land on which he must process hay using either a windrower or hay harvester. For each acre of land, the windrower can process WindrowerHayPerAcre of hay while the hay harvester can process HarvesterHayPerAcre of hay. Per acre, the windrower produces WindrowerMethanePerAcre of methane gas and requires WindrowerFuelPerAcre of fuel. On the other hand, the hay harvester produces HarvesterMethanePerAcre of methane gas per acre and requires HarvesterFuelPerAcre of fuel. There are TotalFuel of fuel available and the farmer can produce at most MaxMethane of methane gas. For how many acres should each machine be used to maximize the amount of hay processed?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: d86d9902-6920-46eb-b41e-6bc007b9d9d9
encoding: FLOAT32
metadata:
{"key": "46", "chroma:document": "A fast food place makes two types of food items. Each 'Wrap' requires 'MeatPerWrap' units of meat and 'RicePerWrap' units of rice, and each 'Platter' requires 'MeatPerPlatter' units of meat and 'RicePerPlatter' units of rice. The time required to make one Wrap is 'TimePerWrap' and the time required to make one Platter is 'TimePerPlatter'. The fast food place must use at least 'MinMeat' units of meat and 'MinRice' units of rice. Additionally, the number of Wraps produced must be at least 'WrapsToPlattersRatio' times the number of Platters produced. The objective is to determine the number of each type of food item to make in order to minimize the total production time."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 0a615f81-cf7e-40a5-919a-75cfb8ed5fdd
encoding: FLOAT32
metadata:
{"key": "47", "chroma:document": "An amusement park is installing ticket machines, both cash-based and card-only machines. A cash-based machine can process CashMachineCapacity people per hour while a card-only machine can process CardMachineCapacity people per hour. The cash-based machine needs CashPaperConsumption rolls of paper per hour while the card-only machine requires CardPaperConsumption rolls of paper per hour. The amusement park needs to be able to process at least MinTotalPeopleRequirement people per hour but can use at most MaxTotalPaperLimit rolls of paper per hour. Also, the number of card-only machines must not exceed the number of cash-based machines."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 9e6aa493-807b-4a72-b41e-f2c7c5ac05bf
encoding: FLOAT32
metadata:
{"key": "48", "chroma:document": "A honey farmer sells his honey in glass and plastic jars. A glass jar can hold HoneyPerGlassJar of honey while a plastic jar can hold HoneyPerPlasticJar of honey. Since glass jars are more expensive, at least MinPlasticPerGlass times as many plastic jars must be filled as glass jars. However, at least MinGlassJars glass jars should be filled. If the farmer has TotalHoney of honey, how many jars of each should be filled to maximize the total number of bottles filled?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 0abbbd1e-d45c-4cb7-b30b-b8558d2e8bac
encoding: FLOAT32
metadata:
{"key": "51", "chroma:document": "A high rise building is buying two types of furnaces, a new model and an old model. A new model furnace has a HeatingCapacityNew and consumes ElectricityConsumptionNew per day. An old model furnace has a HeatingCapacityOld and consumes ElectricityConsumptionOld per day. At most MaxProportionOld of the furnaces can be the old model and at least MinNumNew new model furnaces should be used. The building needs to heat at least TotalApartments and has TotalElectricity available. Determine the number of new and old model furnaces to purchase in order to minimize the total number of furnaces."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: f3d763a1-da63-4628-a2ef-a2b1dff6cefb
encoding: FLOAT32
metadata:
{"key": "52", "chroma:document": "A company needs to determine the number of rural and urban factories to build in order to minimize the total number of factories. A rural factory produces PhonesPerDayRural phones per day and requires ManagersRural managers. An urban factory produces PhonesPerDayUrban phones per day and requires ManagersUrban managers. The company has TotalManagers managers available and must produce at least MinPhonesPerDay phones per day."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: d71a7014-f849-403b-b63e-90664abd74c0
encoding: FLOAT32
metadata:
{"key": "53", "chroma:document": "An ice cream store can buy two types of machines, a counter-top one and a fridge-sized one, to make ice cream. The counter-top machine can produce CounterTopCapacity cones worth of ice cream every day while producing CounterTopHeatOutput units of heat. The fridge-sized machine can produce FridgeCapacity cones worth of ice cream every day while producing FridgeHeatOutput units of heat. The ice cream store can output at most MaxDailyHeatOutput units of heat per day and must produce at least MinDailyProduction cones worth of ice cream. How many of each machine should they buy to minimize the total number of machines needed?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 5696fabc-1788-43d9-808a-90ad5fea28df
encoding: FLOAT32
metadata:
{"key": "54", "chroma:document": "There are NumContainers specialized containers that are used to make a pharmaceutical paste. Each type of container requires WaterRequired of water and PillRequired of powdered pill to produce PasteProduced of paste. The pharmacy has a TotalWater amount of water and a TotalPill amount of powdered pill available. How many of each type of container should be used to maximize the amount of paste that can be made?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: e7c52e7c-e960-49bb-8e00-bce1cbf6ad20
encoding: FLOAT32
metadata:
{"key": "55", "chroma:document": "A company operates on TotalAcres of land where they use oil wells of small and large size. Per acre of land, a small oil well can produce OilProductionSmall units of oil. Per acre of land, a large oil well can produce OilProductionLarge units of oil. However, a small oil well produces PollutionSmall units of pollution and requires DrillBitsSmall drill bits per acre, and a large oil well produces PollutionLarge units of pollution and requires DrillBitsLarge drill bits per acre. The company has TotalDrillBits drill bits available and can produce at most MaxPollution units of pollution due to strict environmental laws. How many acres should be allocated to small and large oil wells to maximize the total oil production?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 0137d890-054a-4b7f-afc6-8a014ff1f5fd
encoding: FLOAT32
metadata:
{"key": "56", "chroma:document": "A bakery makes two types of croissants. The first type of croissant requires ButterAlmond units of butter and FlourAlmond units of flour. The second type of croissant requires ButterPistachio units of butter and FlourPistachio units of flour. The bakery has a total of TotalButter units of butter and TotalFlour units of flour available. The number of the first type of croissants produced should be at least MinRatioAlmondToPistachio times the number of the second type of croissants. The time required to produce one unit of the first type of croissant is TimeAlmond, and the time required to produce one unit of the second type of croissant is TimePistachio. The objective is to determine the number of each type of croissant to produce in order to minimize the total production time."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: d29a0777-0c9c-4096-90f8-0bde285b8abb
encoding: FLOAT32
metadata:
{"key": "57", "chroma:document": "A burger chain is buying both gas and electric grills to make burger patties. A gas grill can cook PattiesPerGasGrill patties per minute while an electric grill can cook PattiesPerElectricGrill patties per minute. The gas grill requires OilPerGasGrill units of cooking oil per minute while the electric grill requires OilPerElectricGrill units of cooking oil per minute. The number of electric grills must be less than the number of gas grills. The burger chain wants to be able to make at least MinPattiesPerMinute patties per minute and use at most MaxOilPerMinute units of cooking oil per minute. How many of each grill should be bought to minimize the total number of grills?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: d9f51d69-f9da-4861-b2bb-4ded755c2cde
encoding: FLOAT32
metadata:
{"key": "58", "chroma:document": "A company sells cough syrup in kids and adult size bottles. A kids size bottle can hold VolumeKids of cough syrup while an adult size bottle can hold VolumeAdult of cough syrup. Since there is no difference in concentration of medical ingredients between the two bottles, the number of adult size bottles must be at least MinRatioAdultToKids times the number of kids size bottles. However, at least MinKidsBottles kids size bottles must be made. If the company has TotalCoughSyrup of cough syrup available, how many bottles of each should be made to maximize the total number of bottles?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: c0467303-ae16-4064-bfa2-07dbfef4eb00
encoding: FLOAT32
metadata:
{"key": "59", "chroma:document": "A bakery makes brownies and lemon squares. Each brownie requires ChocolateMixPerBrownie units of chocolate mix and FiberPerBrownie units of fiber. Each lemon square requires LemonMixPerLemonSquare units of lemon mix and FiberPerLemonSquare units of fiber. Lemon squares sell faster, so the number of lemon squares made must be larger than the number of brownies made. At least MinBrowniesRatio of the items made must be brownies. The bakery has TotalChocolateMix units of chocolate mix and TotalLemonMix units of lemon mix. The goal is to determine the number of each type of item to make in order to minimize the total amount of fiber needed."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: b8a2e65b-34f3-498b-b3fb-f19bb9dee9fb
encoding: FLOAT32
metadata:
{"key": "60", "chroma:document": "A clinic employs nurses and pharmacists to deliver shots to patients. A nurse works NurseHoursPerShift per shift while a pharmacist works PharmacistHoursPerShift per shift. Nurses are paid NursePaymentPerShift per shift while pharmacists are paid PharmacistPaymentPerShift per shift. The clinic needs TotalLaborHoursRequired of healthcare labor to meet needs. If the firm has a budget of TotalBudget, how many of each healthcare worker should be scheduled to minimize the total number of workers?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 07735d1d-46e6-4d31-b258-534821263999
encoding: FLOAT32
metadata:
{"key": "61", "chroma:document": "A laundromat can buy two types of washing machines, a top-loading model and a front-loading model. The top-loading model can wash WashingCapacityTopLoading items per day while the front-loading model can wash WashingCapacityFrontLoading items per day. The top-loading model consumes EnergyConsumptionTopLoading kWh per day while the front-loading model consumes EnergyConsumptionFrontLoading kWh per day. The laundromat must be able to wash at least MinWashingCapacityRequired items per day and has available MaxEnergyAvailable kWh per day. Since the top-loading machines are harder to use, at most MaxPercentageTopLoading of the machines can be top-loading. Further, at least MinFrontLoadingMachines should be front-loading. How many of each machine should the laundromat buy to minimize the total number of washing machines?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: a0a61c8a-364e-4142-bbcd-5401e51aa538
encoding: FLOAT32
metadata:
{"key": "63", "chroma:document": "A shipping company can purchase RegularVans and HybridVans to make deliveries. A RegularVan can deliver RegularVanCapacity packages per day and produces RegularVanPollution units of pollutants. A HybridVan can deliver HybridVanCapacity packages per day and produces HybridVanPollution units of pollutants. Due to a new environmental law, they can produce at most MaxPollution units of pollutants per day. However, the company needs to be able to deliver at least MinPackages packages per day. How many of each type of van should they buy to minimize the total number of vans needed?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 2a297e0a-737a-4a05-88e6-4019dd8b8e6b
encoding: FLOAT32
metadata:
{"key": "64", "chroma:document": "The objective is to maximize the amount of carbon dioxide produced using two different processes: one with a catalyst and one without a catalyst. The process with a catalyst requires 'WoodWithCatalyst' units of wood and 'OxygenWithCatalyst' units of oxygen to produce 'CO2WithCatalyst' units of carbon dioxide. The process without a catalyst requires 'WoodWithoutCatalyst' units of wood and 'OxygenWithoutCatalyst' units of oxygen to produce 'CO2WithoutCatalyst' units of carbon dioxide. The total available resources are 'TotalWood' units of wood and 'TotalOxygen' units of oxygen. The decision variables are the number of times the process with a catalyst is used and the number of times the process without a catalyst is used. The aim is to find the optimal number of each process to maximize the total production of carbon dioxide, subject to the constraints on the availability of wood and oxygen."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 54f78125-7c25-4663-97f0-24ce8d2bb522
encoding: FLOAT32
metadata:
{"key": "65", "chroma:document": "A tea estate has TotalLand acres of land available and they need to pick the tea leaves either using a traditional machine or modern machine. For each acre of land, the traditional machine can pick TealeavesTraditional kg of tea leaves, creates WasteTraditional kg of waste, and requires FuelTraditional liters of fuel. For each acre of land, the modern machine can pick TealeavesModern kg of tea leaves, creates WasteModern kg of waste, and requires FuelModern liters of fuel. The estate has available TotalFuel liters of fuel and can handle at most MaxWaste kg of waste. For how many acres should each machine be used to maximize the amount of tea leaves that can be picked?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: febff883-029e-405d-9dff-aa1b41cbd744
encoding: FLOAT32
metadata:
{"key": "67", "chroma:document": "An organization is purchasing 2 different models of stamping machines. Each model has a specific StampingRate and GlueConsumption per minute. The number of the first model of machines must be less than the number of the second model. Additionally, the organization aims to ensure they can process at least MinLetters letters per minute and use at most MaxGlue units of glue per minute. The objective is to determine the number of each model of stamping machines to minimize the total number of stamping machines."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 48ae4c6c-c32f-48ed-9fb7-38ccdd1ec330
encoding: FLOAT32
metadata:
{"key": "68", "chroma:document": "A company sells their bananas in small and large crates. A small crate can hold BananasPerSmallCrate bananas while a large crate can hold BananasPerLargeCrate bananas. The number of large crates must be at least MinLargeToSmallRatio times the number of small crates. However, at least MinSmallCrates small crates should be used. If the company has TotalBananas available bananas, how many of each crate should the company use to maximize the total number of crates used?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 59a4c36d-32ff-43c3-b6b9-b7be9234230d
encoding: FLOAT32
metadata:
{"key": "69", "chroma:document": "A store sells two types of crepes: chocolate crepes and peanut butter crepes. A chocolate crepe requires ChocolateSpreadForChocolateCrepe units of chocolate spread and CrepeMixForChocolateCrepe units of crepe mix. A peanut butter crepe requires PeanutButterSpreadForPeanutButterCrepe units of peanut butter spread and CrepeMixForPeanutButterCrepe units of crepe mix. The number of peanut butter crepes made (NumPeanutButterCrepes) must exceed the number of chocolate crepes made (NumChocolateCrepes). Additionally, at least MinimumChocolateCrepeProportion of the total crepes made should be chocolate crepes, i.e., NumChocolateCrepes should be at least MinimumChocolateCrepeProportion * (NumChocolateCrepes + NumPeanutButterCrepes). The store has TotalChocolateSpread units of chocolate spread and TotalPeanutButterSpread units of peanut butter spread available. The total amount of chocolate spread used by all chocolate crepes must not exceed TotalChocolateSpread, and the total amount of peanut butter spread used by all peanut butter crepes must not exceed TotalPeanutButterSpread. The objective is to determine NumChocolateCrepes and NumPeanutButterCrepes to minimize the total amount of crepe mix needed while satisfying these constraints."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: b64e8154-5d4f-4394-8cb0-1c74d33f331b
encoding: FLOAT32
metadata:
{"key": "70", "chroma:document": "A fire department employs regular and emergency fire fighters. A regular fire fighter works HoursRegularShift per shift and earns EarningsRegular. An emergency fire fighter works HoursEmergencyShift per shift and earns EarningsEmergency. Due to wildfires in the region, the fire department needs at least MinHoursRequired hours of fire fighter time. If the fire department has a budget of Budget, how many of each should the fire department hire to minimize the total number of fire fighters?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 5eda92f4-9ad8-44dd-a165-aa5479f6a0b4
encoding: FLOAT32
metadata:
{"key": "71", "chroma:document": "A mall buys two types of hand sanitizer machines, which have delivery rates defined by 'DeliverRate' and energy consumptions defined by 'EnergyConsumption'. Due to hygiene concerns, at most 'MaxManualPercentage' of the machines can be manual, and at least 'MinMotionActivated' must be motion activated. The mall must achieve a minimum total delivery rate of 'MinDeliverRate' and adhere to a maximum total energy consumption of 'MaxEnergyConsumption'. The goal is to determine the number of each type of machine to minimize the total number of machines."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 458c08af-907c-43d7-8f19-c0373592f106
encoding: FLOAT32
metadata:
{"key": "72", "chroma:document": "A company can build two types of shops: a small shop and a large shop. A small shop can produce HotDogsPerDaySmallShop hot dogs per day and requires WorkersPerSmallShop workers. A large shop can produce HotDogsPerDayLargeShop hot dogs per day and requires WorkersPerLargeShop workers. The company must produce at least MinHotDogsPerDay hot dogs per day but only has TotalWorkers workers available. How many of each type of shop should the company build to minimize the total number of shops?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 4b8b5c82-2c63-4039-9cea-820ebc1e3711
encoding: FLOAT32
metadata:
{"key": "73", "chroma:document": "An airport buys two types of vehicles, a 4-wheeler and 3-wheeler, to help move luggage. A 4-wheeler vehicle can move LuggageCapacity4Wheeler luggage per day and produces Pollution4Wheeler units of pollutant per day. A 3-wheeler vehicle can move LuggageCapacity3Wheeler luggage per day and produces Pollution3Wheeler units of pollutant per day. The airport needs to be able to move at least MinLuggage luggage per day. To avoid over-polluting the airport, they can produce at most MaxPollution units of pollutant per day. How many of each vehicle should the airport buy to minimize the total number of vehicles needed."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 9e9c0a8d-3bde-4a4c-90f2-5c2ab977eedf
encoding: FLOAT32
metadata:
{"key": "75", "chroma:document": "A man fishes in a TotalArea lake and can catch fish either using a net or fishing line. For each acre of the lake, using a net will catch FishCaughtNet fish and requires BaitRequiredNet units of bait but also causes PainNet units of pain for the fisherman. For each acre of the lake, using a fishing line will catch FishCaughtLine fish and requires BaitRequiredLine units of bait but also causes PainLine units of pain for the fisherman. The fisherman has available TotalBait units of bait and can tolerate at most MaxPain units of pain. For how many acres each should he use each fishing method to maximize the amount of fish he can catch?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: ecec7de4-540f-445d-a060-f43ca659e806
encoding: FLOAT32
metadata:
{"key": "76", "chroma:document": "A coffee shop sells two types of coffee: mochas and regular coffees. Each type requires specific units of coffee powder (CoffeePowderPerMocha, CoffeePowderPerRegular) and milk (MilkPerMocha, MilkPerRegular), which are limited in total availability (TotalCoffeePowder, TotalMilk). Producing each type also requires a specific amount of time (TimePerMocha, TimePerRegular). Additionally, there is a constraint specifying that the number of mochas made must be at least a certain multiple (MochaToRegularRatio) of the number of regular coffees made. The goal is to determine the number of each type of coffee to produce in order to minimize the total production time, given these constraints."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 1850064e-98c5-4edd-b3fe-7bc7bcd3c3b6
encoding: FLOAT32
metadata:
{"key": "77", "chroma:document": "A butcher shop is buying slicers for their shop, a manual slicer and an automatic slicer. The manual slicer has a Cutting Rate (ManualCutRate) and uses grease at a rate (ManualGreaseRate). The automatic slicer has a Cutting Rate (AutomaticCutRate) and uses grease at a rate (AutomaticGreaseRate). The number of manual slicers should be less than the number of automatic slicers. The butcher shop must meet a minimum requirement of slices per minute (MinSlices) and adhere to a maximum grease usage per minute (MaxGrease). The goal is to determine the number of each slicer to minimize the total number of slicers in the shop."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 276ff71b-4ee1-44bf-ab74-6af85a8a6fa6
encoding: FLOAT32
metadata:
{"key": "78", "chroma:document": "A water company sells water in glass and plastic bottles. A glass bottle can hold GlassBottleCapacity of water while a plastic bottle can hold PlasticBottleCapacity of water. Because most customers prefer plastic bottles, the number of plastic bottles must be at least MinPlasticToGlassRatio times the number of glass bottles. However, there must be at least MinGlassBottles glass bottles. If the company has available TotalWater of water, how many of each bottle should be made to maximize the total number of bottles?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 5bcc420d-7353-4749-ab25-a8de1ae9f471
encoding: FLOAT32
metadata:
{"key": "79", "chroma:document": "A restaurant makes two types of curry: goat curry and chicken curry. Each bowl of goat curry requires GoatMeatPerGoatCurry units of goat meat and CurryBasePerGoatCurry units of curry base. Each bowl of chicken curry requires ChickenMeatPerChickenCurry units of chicken meat and CurryBasePerChickenCurry units of curry base. The restaurant has TotalGoatMeat units of goat meat and TotalChickenMeat units of chicken meat available. At least MinChickenCurryPercentage percentage of the total bowls made must be chicken curry, and the number of goat curry bowls must be larger than the number of chicken curry bowls. The objective is to determine the number of each type of curry bowl to make so as to minimize the total usage of curry base."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: cba5b30c-4ba6-4d13-bb78-26d014ecdd32
encoding: FLOAT32
metadata:
{"key": "80", "chroma:document": "An accounting firm employs part time workers and full time workers. Full time workers work HoursPerShiftFullTime per shift while part time workers work HoursPerShiftPartTime per shift. In addition, full time workers are paid WageFullTime per shift while part time workers are paid WagePartTime per shift. Currently, the accounting firm has a project requiring TotalLaborHours of labor. If the firm has a TotalBudget for wages, determine the number of each type of worker to schedule in order to minimize the total number of workers, subject to the constraints of meeting the required labor hours and the budget."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 01b9f586-1bc9-4f7e-a609-fbf056525f39
encoding: FLOAT32
metadata:
{"key": "81", "chroma:document": "A factory has two types of machines. Each machine of the first type can produce ItemsMachineA items and consumes ElectricityMachineA kWh per day. Each machine of the second type can produce ItemsMachineB items and consumes ElectricityMachineB kWh per day. The factory needs to produce at least MinItemsPerDay items per day and has MaxElectricityPerDay kWh of electricity available per day. At most MaxPercentageB of the machines can be of the second type. Additionally, at least MinMachinesA of the machines must be of the first type. The objective is to find the number of each type of machine to use to minimize the total number of machines."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: e3ff8f39-2cae-4f3c-9b2c-748297eec05d
encoding: FLOAT32
metadata:
{"key": "83", "chroma:document": "A chemical plant can buy two types of generators, generator A and generator B, which use two different processes to generate hydrogen. Generator A uses an electrolysis process and produces HydrogenProductionA of hydrogen as well as PollutantProductionA of pollutants every day. Generator B uses a fermentation process to produce HydrogenProductionB of hydrogen per day while outputting PollutantProductionB of pollutants. The chemical plant must make a minimum of MinHydrogenRequirement of hydrogen per day but due to environmental restrictions they can produce at most MaxPollutantAllowance of pollutant. The goal is to determine the quantities, CountA and CountB, of each type of generator to minimize the total number of generators needed."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 19d92935-5902-41b4-85d4-a790f1b9c33d
encoding: FLOAT32
metadata:
{"key": "84", "chroma:document": "There are two chemical reactions, chemical reaction A and chemical reaction B. Chemical reaction A requires InertGasA units of rare inert gas and TreatedWaterA units of treated water to produce CompoundA units of a rare compound. Chemical reaction B requires InertGasB units of rare inert gas and TreatedWaterB units of treated water to produce CompoundB units of a rare compound. There are TotalInertGas units of rare inert gas and TotalTreatedWater units of treated water available in the lab. The objective is to determine the number of reactions of type A (XA) and type B (XB) to maximize the total amount of the rare compound produced."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 5515dcc5-55ed-4601-b249-dfdb29ed9eb5
encoding: FLOAT32
metadata:
{"key": "85", "chroma:document": "A mining company has available TotalLand square miles of mining sites and is considering the use of two mining techniques: heap leaching and vat leaching. For each square mile of land, heap leaching technique can have a daily production of HeapLeachingProduction of rare earth oxide per square mile but it also creates HeapLeachingWastewater of polluted wastewater and requires HeapLeachingMachines of extraction machines. On the other hand, vat leaching technique produces VatLeachingProduction of rare earth oxide per square mile per day while creating VatLeachingWastewater of polluted wastewater and requiring VatLeachingMachines of extraction machines. There are TotalMachines available and due to environmental regulations, the amount of polluted wastewater must be at most MaxWastewater daily. Find the proportion of lands that use each mining technique in order to maximize the daily production of rare earth oxide."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 1b410118-d508-4142-86bf-728f230d7779
encoding: FLOAT32
metadata:
{"key": "86", "chroma:document": "A small chocolate shop makes two types of chocolate bars: milk and dark. Milk chocolate bars require CocoaPerMilkChocolate units of cocoa and MilkPerMilkChocolate units of milk. Dark chocolate bars require CocoaPerDarkChocolate units of cocoa and MilkPerDarkChocolate units of milk. The shop has TotalCocoa units of cocoa and TotalMilk units of milk available. Additionally, at least MilkToDarkRatio times as many milk chocolate bars need to be produced as dark chocolate bars. To minimize the total production time, where producing one milk chocolate bar takes TimePerMilkChocolate minutes and one dark chocolate bar takes TimePerDarkChocolate minutes, how many of each type of chocolate bar should be produced?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 8108c23f-4892-4386-8ce8-092d2779acda
encoding: FLOAT32
metadata:
{"key": "87", "chroma:document": "An office is buying two types of printers: a premium model and a regular model. The premium model can print PagesPerMinutePremium pages per minute and the regular model can print PagesPerMinuteRegular pages per minute. Additionally, the premium model requires InkPerMinutePremium units of ink per minute, while the regular model requires InkPerMinuteRegular units of ink per minute. The office wants to ensure at least MinPagesPerMinute pages can be printed per minute, and at most MaxInkPerMinute units of ink can be used per minute. The number of regular printers must be less than the number of premium printers to minimize the total number of printers in the office."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: f0882597-92f8-4746-b061-ae8ba4e40eb4
encoding: FLOAT32
metadata:
{"key": "88", "chroma:document": "A company sells two types of bottles: a vintage bottle with volume VolumeVintage and a regular bottle with volume VolumeRegular. The company has a total available volume of TotalVolume. The number of regular bottles must be at least MinRatioRegularToVintage times the number of vintage bottles. Additionally, there is a requirement to produce at least MinVintageBottles vintage bottles. The goal is to determine how many of each type of bottle should be produced in order to maximize the total number of bottles."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: fe15e5ab-f8c2-4196-b1ad-1acbc1a81893
encoding: FLOAT32
metadata:
{"key": "90", "chroma:document": "A patient in the hospital can take two pills, Pill 1 and Pill 2. Per pill, Pill 1 provides PainMedPill1 units of pain medication and AnxietyMedPill1 units of anxiety medication. Per pill, Pill 2 provides PainMedPill2 units of pain medication and AnxietyMedPill2 units of anxiety medication. In addition, Pill 1 causes DischargePill1 units of discharge while Pill 2 causes DischargePill2 units of discharge. At most MaxPainMed units of pain medication can be provided and at least MinAnxietyMed units of anxiety medication must be provided. How many pills of each should the patient be given to minimize the total amount of discharge?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: d8f3cffe-7d52-4563-8f40-d4719ecb94bd
encoding: FLOAT32
metadata:
{"key": "91", "chroma:document": "A man on a strict diet consumes drinks from two brands, alpha and omega. Each alpha brand drink contains ProteinAlpha grams of protein, SugarAlpha grams of sugar, and CaloriesAlpha calories per bottle. Each omega brand drink contains ProteinOmega grams of protein, SugarOmega grams of sugar, and CaloriesOmega calories per bottle. The man wants to consume at least MinProtein grams of protein and MinCalories calories. Additionally, the omega brand drink should constitute at most MaxOmegaProportion of his total drink intake. The goal is to find the number of bottles of each brand he should drink to minimize his sugar intake."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 0cd1cfe8-d7e0-4525-9d96-227d989b6e7d
encoding: FLOAT32
metadata:
{"key": "92", "chroma:document": "A summer camp conducts science experiments using NumBeakers different types of beakers. Each beaker i requires FlourRequired[i] units of flour and LiquidRequired[i] units of special liquid to produce SlimeProduced[i] units of slime, and generates WasteProduced[i] units of waste. The summer camp has a total of TotalFlour units of flour and TotalLiquid units of special liquid available. The maximum allowable waste that can be produced is MaxWaste units. The goal is to determine the number of each beaker type to use in order to maximize the total amount of slime produced."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 7a90f95a-a3d6-4ed9-aa69-efd61b08b173
encoding: FLOAT32
metadata:
{"key": "93", "chroma:document": "A dog hospital has TotalToothMedication units of tooth medication to make both small and large bones. A small bone requires ToothMedicationSmall units of tooth medication and MeatSmall units of meat. A large bone requires ToothMedicationLarge units of tooth medication and MeatLarge units of meat. Since most dogs prefer small bones, at least MinPercentageSmallBones percent of the bones made must be small. In addition, the hospital must make at least MinLargeBones large bones. How many of each bone should be made to minimize the amount of meat needed?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 31956227-28d0-4620-9104-0b2bdcea79d6
encoding: FLOAT32
metadata:
{"key": "94", "chroma:document": "A scientist in the arctic needs to consume enough vitamin D and vitamin C by drinking two types of juice: orange juice and apple juice. Each box of orange juice contains VitDOrangeJuice units of vitamin D and VitCOrangeJuice units of vitamin C. Each box of apple juice contains VitDAppleJuice units of vitamin D and VitCAppleJuice units of vitamin C. Since the scientist prefers apple juice, he must drink at least MinAppleToOrangeRatio times the number of apple juice boxes as the number of orange juice boxes. However, he must also drink at least MinOrangeJuice boxes of orange juice. To avoid a vitamin C overdose, the scientist can consume at most MaxVitaminC units of vitamin C. The objective is to determine the number of each type of juice box the scientist should drink to maximize his total vitamin D intake."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 86f2339a-6b4c-4501-b9de-e90071789d9e
encoding: FLOAT32
metadata:
{"key": "95", "chroma:document": "A cleaning company uses a cleansing chemical and odor-removing chemical to clean a house. Each unit of the cleansing chemical takes CleansingTimePerUnit to be effective while each unit of the odor-removing chemical takes OdorRemovingTimePerUnit to be effective. The company must use at least MinCleansingChemical of the cleansing chemical. In total, at least MinTotalChemicals of chemicals must be used per house. Further, because the cleansing chemical is strong, there can be at most MaxCleansingToOdorRatio times the amount of odor-removing chemical as cleansing chemical. The objective is to determine the number of units of each chemical to minimize the total time it takes for a house to be cleaned."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 5ef0b674-60fe-4da6-862e-82c676919d1e
encoding: FLOAT32
metadata:
{"key": "96", "chroma:document": "A drug company is producing two types of pills: allergy pills and fever reducing pills, using two factories: factory 1 and factory 2. Factory 1 produces AllergyPillsPerHourFactory1 allergy pills and FeverPillsPerHourFactory1 fever reducing pills per hour, requiring CompoundPerHourFactory1 units of a rare compound per hour. Factory 2 produces AllergyPillsPerHourFactory2 allergy pills and FeverPillsPerHourFactory2 fever reducing pills per hour, requiring CompoundPerHourFactory2 units of the rare compound per hour. The company has TotalCompoundAvailable units of the rare compound available. The company must produce at least MinAllergyPills allergy pills and MinFeverPills fever reducing pills. The objective is to determine the number of hours each factory should operate to minimize the total operating time while satisfying all constraints."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 416c5a62-2303-40d9-90f5-0550950f0497
encoding: FLOAT32
metadata:
{"key": "99", "chroma:document": "A clinic takes patient blood pressure either using an automatic machine or a manual machine. The automatic machine takes TimeAutomatic per patient while the manual machine takes TimeManual per patient. Since the automatic machine frequently breaks, at least ManualToAutomaticRatio times the number of patients processed by the automatic machine must have their blood pressure taken by the manual machine. However, at least MinPatientsAutomatic patients can be processed by the automatic machine. If the clinic is open for TotalTime, maximize the number of patients whose blood pressure can be taken."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: a78e7dd0-0a39-42bf-9ab5-77911727bf84
encoding: FLOAT32
metadata:
{"key": "100", "chroma:document": "A patient with a sore throat can drink NumSyrups different syrups for treatment. Each serving of syrup i delivers MedicineToThroat[i] units of medicine to the throat and MedicineToLungs[i] units of medicine to the lungs. Furthermore, each serving of syrup i contains SugarContent[i] units of sugar. The patient can get at most MaxMedicineThroat units of medicine for the throat and at least MinMedicineLungs units of medicine to the lungs. How many servings of each syrup should the patient take to minimize their sugar intake?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 8902a579-c7b0-45cf-beae-9287615905ca
encoding: FLOAT32
metadata:
{"key": "102", "chroma:document": "A science show performs NumDemos different demonstrations. Demonstration i requires MintRequirement[i] units of mint and ActiveRequirement[i] units of active ingredient to produce MintyFoamProduced[i] units of minty foam. Additionally, demonstration i produces BlackTarProduced[i] units of black tar. The show has AvailableMint units of mint and AvailableActive units of active ingredient available. The maximum allowable production of black tar is MaxBlackTar units. The task is to determine the optimal number of each demonstration to maximize the total amount of minty foam produced, without exceeding the available resources and the maximum allowable black tar."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: a403b24c-c1a4-42dc-9426-e00204f8ca98
encoding: FLOAT32
metadata:
{"key": "104", "chroma:document": "A parent feeds their baby two flavors of baby food, apple and carrot, in order to meet the baby's fat and folate requirements. Each serving of apple flavored baby food contains FatPerAppleServing units of fat and FolatePerAppleServing units of folate. Each serving of carrot flavored baby food contains FatPerCarrotServing units of fat and FolatePerCarrotServing units of folate. The baby does not like the carrot flavor, and therefore he must eat AppleCarrotConsumptionRatio times as many apple flavored baby food servings as carrot flavored baby food servings. However, he must eat at least MinCarrotServings servings of carrot flavored baby food. If the baby can consume at most MaxFolate units of folate, how many servings of each should he eat to maximize his fat intake?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 44ede99c-11a5-4bf5-acf9-6f5dbced04d7
encoding: FLOAT32
metadata:
{"key": "106", "chroma:document": "A pharmacy has NumFactories factories, where they make NumProducts different products. Each factory produces ProductionRate of each product per hour. Each factory also requires BaseGelRequirement units of base gel per hour. The pharmacy has AvailableBaseGel units of base gel available. Further, they must make at least MinProduction of each product. The goal is to determine how many hours each factory should be run to meet the minimum production requirements and minimize the total time needed."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: f614ff26-6551-4667-aa94-3e9128a2fcd3
encoding: FLOAT32
metadata:
{"key": "107", "chroma:document": "A man needs to consume at least a minimum required number of units of fat (RequiredFat) and a minimum required number of calories (RequiredCalories) by eating burgers and slices of pizza. Each burger contains given units of fat (FatPerBurger), calories (CaloriesPerBurger), and cholesterol (CholesterolPerBurger). Each slice of pizza contains given units of fat (FatPerPizza), calories (CaloriesPerPizza), and cholesterol (CholesterolPerPizza). He needs to consume at least twice as many slices of pizza as burgers (PizzaToBurgerRatio) and wants to minimize his cholesterol intake."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 5b8d0ea1-61db-4110-92e1-9af59ba660a1
encoding: FLOAT32
metadata:
{"key": "108", "chroma:document": "A clinic makes two types of vitamin batches: shots and pills. Each batch of vitamin shots requires UnitCShots units of vitamin C and UnitDShots units of vitamin D. Each batch of vitamin pills requires UnitCPills units of vitamin C and UnitDPills units of vitamin D. The number of batches of vitamin pills (NumBatchesPills) must be larger than the number of batches of vitamin shots (NumBatchesShots). The clinic can make at most UpperLimitBatchesShots batches of vitamin shots. The clinic has AvailableC units of vitamin C and AvailableD units of vitamin D. Each batch of vitamin shots supplies SupplyShots people and each batch of vitamin pills supplies SupplyPills people. The goal is to determine the number of batches of each type (NumBatchesShots and NumBatchesPills) to maximize the number of people that can be supplied."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 851df60f-02e4-4041-a0e9-81ed418b3729
encoding: FLOAT32
metadata:
{"key": "109", "chroma:document": "A doctor's office takes the temperature of patients one by one either by using an electronic or regular thermometer. The electronic thermometer takes ElectronicThermometerTime to make a reading while the regular thermometer takes RegularThermometerTime to make a reading. Since the electronic thermometer is more accurate, at least MinElectronicRegularRatio times as many patients should have their temperature checked by the electronic thermometer than the regular thermometer. Since the electronic thermometer has a cooldown time, at least MinRegularPatients patients should have their temperature checked by a regular thermometer. If the office is open for TotalOpenTime, maximize the total number of patients whose temperature is taken."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 1b55f660-12da-471b-a128-b36099d2f61d
encoding: FLOAT32
metadata:
{"key": "110", "chroma:document": "A patient can be hooked up to two machines to have medicine delivered, machine 1 and machine 2. Machine 1 delivers MedicineDeliveryRateMachine1Heart units of medicine to the heart per minute and MedicineDeliveryRateMachine1Brain units of medicine per minute to the brain. Machine 2 delivers MedicineDeliveryRateMachine2Heart units of medicine per minute to the heart and MedicineDeliveryRateMachine2Brain units of medicine per minute to the brain. In addition however, machine 1 creates WasteProductionRateMachine1 units of waste per minute while machine 2 creates WasteProductionRateMachine2 units of waste per minute. If at most MaxMedicineHeart units of medicine can be received by the heart and at least MinMedicineBrain units of medicine should be received by the brain, how many minutes should each machine be used to minimize the total amount of waste produced?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 63da8e40-201f-4d43-9a32-278cae5a4c19
encoding: FLOAT32
metadata:
{"key": "111", "chroma:document": "A travelling salesman consumes packs of ramen and fries. Each pack of ramen provides RamenCalories, RamenProtein, and RamenSodium. Each pack of fries provides FriesCalories, FriesProtein, and FriesSodium. The salesman has NumMeals meals, and at most MaxRamenPercentage of these meals can be ramen. The salesman needs to consume at least MinCalories and MinProtein in total across all meals and seeks to minimize his sodium intake."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 46b16442-78d7-40a9-a59f-265010518337
encoding: FLOAT32
metadata:
{"key": "112", "chroma:document": "A science store produces two types of boxes, a cheap box and an expensive box. Each cheap box requires MetalCheapBox units of metal and AcidCheapBox units of acid to produce FoamCheapBox units of foam, while giving off HeatCheapBox units of heat. Each expensive box requires MetalExpensiveBox units of metal and AcidExpensiveBox units of acid to produce FoamExpensiveBox units of foam, while giving off HeatExpensiveBox units of heat. The store has TotalMetal units of metal and TotalAcid units of acid available. The total heat given off by the boxes cannot exceed MaxHeat units. The objective is to determine the number of each type of box to produce in order to maximize the total foam produced."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 0cb030f5-b2ea-4701-b705-cc1b808d413c
encoding: FLOAT32
metadata:
{"key": "117", "chroma:document": "A woman eats servings of almonds and servings of cashews to meet her weekly intake of MinimumCalories calories and MinimumProtein grams of protein. A serving of almonds provides CaloriesAlmonds calories, ProteinAlmonds grams of protein, and FatAlmonds grams of fat. A serving of cashews provides CaloriesCashews calories, ProteinCashews grams of protein, and FatCashews grams of fat. The woman must consume at least MinimumAlmondCashewRatio times as many servings of almonds as cashews. The objective is to determine the number of servings of almonds and cashews she should eat to minimize her fat intake."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 6e93e606-a07a-4dce-bd23-a7f35f6c898a
encoding: FLOAT32
metadata:
{"key": "118", "chroma:document": "A company makes LiquidSanitizer and FoamSanitizer. Each LiquidSanitizer requires WaterLiquidSanitizer units of water and AlcoholLiquidSanitizer units of alcohol. Each FoamSanitizer requires WaterFoamSanitizer units of water and AlcoholFoamSanitizer units of alcohol. The company has TotalWater units of water and TotalAlcohol units of alcohol available. The number of FoamSanitizer made must be greater than the number of LiquidSanitizer. Additionally, at most MaxLiquidSanitizer units of LiquidSanitizer can be made. Each LiquidSanitizer can clean HandsCleanedByLiquid hands and each FoamSanitizer can clean HandsCleanedByFoam hands. The objective is to determine the number of LiquidSanitizer and FoamSanitizer to produce to maximize the total number of hands that can be cleaned."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: aa10d0fc-1ea0-459e-adcd-968689e8c7bb
encoding: FLOAT32
metadata:
{"key": "120", "chroma:document": "A patient in the hospital can take two different pain killers, pain killer 1 and pain killer 2. Per dose, pain killer 1 delivers LegsMedicinePainKiller1 units of medicine to the legs and BackMedicinePainKiller1 units of medicine to the back. Per dose, pain killer 2 delivers LegsMedicinePainKiller2 units of medicine to the legs and BackMedicinePainKiller2 units of medicine to the back. In addition, pain killer 1 delivers SleepMedicinePainKiller1 units of sleeping medicine and pain killer 2 delivers SleepMedicinePainKiller2 units of sleeping medicine. At most MaxSleepMedicine units of sleeping medicine should be delivered, and at least MinLegsMedicine units of medicine should be delivered to the legs. The goal is to determine the number of doses of each pain killer that should be taken to maximize the amount of medicine delivered to the back."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: df390ad2-ee9b-43e6-a953-a6442e58e980
encoding: FLOAT32
metadata:
{"key": "123", "chroma:document": "A pharmaceutical company has TotalPainkillerMedicine units of painkiller medicine and makes daytime and nighttime painkiller pills. A daytime pill has PainkillerInDaytimePill units of painkiller medicine and SleepMedicineInDaytimePill units of sleep medicine. A nighttime pill has PainkillerInNighttimePill units of painkiller medicine and SleepMedicineInNighttimePill units of sleep medicine. Since some people don\u2019t want the sleeping effect, at least MinPercentageDaytimePills percent of the pills must be daytime pills. However at least MinNighttimePills nighttime pills must be made. The objective is to determine the number of each pill that should be made to minimize the total amount of sleep medicine required."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 4f4016eb-5579-4987-b9d5-218d55294fac
encoding: FLOAT32
metadata:
{"key": "124", "chroma:document": "A competitive eater challenges himself to eat slices of cheesecake and caramel cake. Each slice of cheesecake contains CaloriesCheesecake and SugarCheesecake. Each slice of caramel cake contains CaloriesCaramelCake and SugarCaramelCake. He prefers cheesecake and decides to eat at least MinCheesecakeRatio times as many slices of cheesecake as there are slices of caramel cake. However, he must also eat at least MinCaramelSlices slices of caramel cake. If he can consume at most MaxCalories in one day, how many slices of each cake should he eat to maximize the total amount of sugar he consumes?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 2c8f0752-4bc9-42f1-ae98-608ddc46c664
encoding: FLOAT32
metadata:
{"key": "127", "chroma:document": "A patient needs to determine the optimal number of oranges and grapefruits to eat in order to minimize their sugar intake. One orange contains VitCOranges units of vitamin C, VitAOranges units of vitamin A, and SugarOranges grams of sugar. One grapefruit contains VitCGrapefruit units of vitamin C, VitAGrapefruit units of vitamin A, and SugarGrapefruit grams of sugar. The patient must get at least MinVitC units of vitamin C and MinVitA units of vitamin A. Additionally, the patient must consume at least 2 times as many oranges as grapefruits."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 963373a9-a8ec-4110-a05d-68f21715ce20
encoding: FLOAT32
metadata:
{"key": "130", "chroma:document": "A patient is undergoing radiation treatment involving two beams, Beam1 and Beam2. Beam1 delivers DoseBeam1Pancreas units of medicine per minute to the benign area of the pancreas and DoseBeam1Skin units of medicine per minute to the benign area of the skin. Beam2 delivers DoseBeam2Pancreas units of medicine per minute to the benign area of the pancreas and DoseBeam2Skin units of medicine per minute to the benign area of the skin. In addition, Beam1 delivers DoseBeam1Tumor units of medicine per minute to the tumor and Beam2 delivers DoseBeam2Tumor units of medicine per minute to the tumor. At most MaxDoseSkin units of medicine should be received by the skin and at least MinDoseTumor units of medicine should be delivered to the tumor. The objective is to determine how many minutes of each beam, denoted as TimeBeam1 and TimeBeam2, should be used to minimize the total radiation received by the pancreas. This requires solving an optimization problem with the constraints TimeBeam1 \u2265 0 and TimeBeam2 \u2265 0."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 61982fe7-ddbb-4a0a-8a53-0a71bfd70ee9
encoding: FLOAT32
metadata:
{"key": "131", "chroma:document": "A body builder buys pre prepared meals, a turkey dinner and a tuna salad sandwich. The turkey dinner contains ProteinTurkeyDinner grams of protein, CarbsTurkeyDinner grams of carbs, and FatTurkeyDinner grams of fat. The tuna salad sandwich contains ProteinTunaSandwich grams of protein, CarbsTunaSandwich grams of carbs, and FatTunaSandwich grams of fat. The bodybuilder wants to get at least MinProtein grams of protein and MinCarbs grams of carbs. In addition, because the turkey dinner is expensive, at most MaxPercentTurkeyDinner percent of the meals should be turkey dinner. How many of each meal should he eat if he wants to minimize his fat intake?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 40aa8fd8-42a7-480c-8aa9-3c9ebb2e5f05
encoding: FLOAT32
metadata:
{"key": "132", "chroma:document": "A chemistry teacher teaches her students two experiments, experiment 1 and experiment 2. In experiment 1, RedLiquidExp1 units of the red liquid and BlueLiquidExp1 units of the blue liquid mix to create GreenGasExp1 units of green gas. In experiment 2, RedLiquidExp2 units of the red liquid and BlueLiquidExp2 units of the blue liquid mix to create GreenGasExp2 units of green gas. In addition, experiment 1 produces SmellyGasExp1 units of smelly gas while experiment 2 produces SmellyGasExp2 units of smelly gas. The lab has available TotalRedLiquid units of red liquid and TotalBlueLiquid units of blue liquid. If at most MaxSmellyGas units of smelly gas can be produced, how many experiments of each should be done to maximize the total amount of green gas produced?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: ee41a64d-a881-4cf9-a88f-9c6325f2d700
encoding: FLOAT32
metadata:
{"key": "135", "chroma:document": "A drug company is making pain killers and sleeping pills using two processes, Process1 and Process2. Process1 produces PainKillers1 units of pain killers and SleepingPills1 units of sleeping pills per hour. Process2 produces PainKillers2 units of pain killers and SleepingPills2 units of sleeping pills per hour. Process1 requires Material1 units of preliminary material while Process2 requires Material2 units of preliminary material. The drug company has AvailableMaterial units of preliminary material and must produce at least MinPainKillers units of pain killers and MinSleepingPills units of sleeping pills. The goal is to determine how many hours each of Process1 and Process2 should be run to meet the production requirements while minimizing the total hours of operation."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 7341c22a-7cca-41e0-8530-a6b90cf24198
encoding: FLOAT32
metadata:
{"key": "136", "chroma:document": "A dietician recommends her client eat blueberries and strawberries to meet her anti-oxidant and mineral requirement. A pack of blueberries contains AntioxidantsBlueberries units of anti-oxidants and MineralsBlueberries units of minerals. A pack of strawberries contains AntioxidantsStrawberries units of anti-oxidants and MineralsStrawberries units of minerals. The client must get at least MinAntioxidants units of anti-oxidants and MinMinerals units of minerals. In addition, because blueberries are not in season, the dietician recommends she eats at least MinRatioStrawberriesBlueberries times as many packs of strawberries as blueberries. If a pack of blueberries contains SugarBlueberries grams of sugar and a pack of strawberries contains SugarStrawberries grams of sugar, how many packs of each should she consume to minimize her sugar intake?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 55f60fe7-ea13-4847-b3d2-1f8ceda53b4e
encoding: FLOAT32
metadata:
{"key": "139", "chroma:document": "A company can transport their boxes using their own vans or by renting trucks. Their vans can transport BoxesPerVan per trip while a truck can transport BoxesPerTruck per trip. Since they own their vans, the cost per van trip is CostPerVan while the cost per truck trip is CostPerTruck. The company needs to transport at least MinBoxes and they have a budget of MaxBudget. Since the vans also provide advertising, the number of trips by van must be larger than the number of trips by trucks. How many trips by each should be done to minimize the total number of trips?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 33cf3b21-843a-431c-b8e5-32933154037d
encoding: FLOAT32
metadata:
{"key": "140", "chroma:document": "A farmer transports his honey in two types of bottles, small and large. A small bottle has a capacity of SmallBottleCapacity units of honey while a large bottle has a capacity of LargeBottleCapacity units of honey. There are at most MaxSmallBottles small bottles and MaxLargeBottles large bottles available. The farmer must use at least twice as many small bottles as large bottles. Additionally, the total number of bottles used must not exceed MaxTotalBottles, and at least MinLargeBottles bottles must be large. The objective is to determine the number of each type of bottle to use to maximize the total amount of honey transported."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: e712b507-045c-4e43-86b3-8554c151e361
encoding: FLOAT32
metadata:
{"key": "141", "chroma:document": "An international goods exporter uses ships and planes to transport goods. A ship can take ShipCapacity containers worth of goods and uses ShipFuel liters of fuel per trip. A plane can take PlaneCapacity containers worth of goods and uses PlaneFuel liters of fuel per trip. The company needs to transport at least MinContainers containers worth of goods. In addition, there can be at most MaxPlaneTrips plane trips made and a minimum of MinShipPercentage fraction of the trips must be made by ship. How many of each trip should be made to minimize the total amount of fuel consumed?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 1644bf58-82ef-441f-b3a9-71f0af6e946d
encoding: FLOAT32
metadata:
{"key": "142", "chroma:document": "The objective is to minimize the total amount of time needed to transport a certain number of ducks using two transportation methods: boats and canoes. Each boat can take BoatDucksPerTrip ducks per trip and takes BoatTripTime minutes per trip. Each canoe can take CanoeDucksPerTrip ducks per trip and takes CanoeTripTime minutes per trip. There is a maximum limit of MaxBoatTrips boat trips allowed, and at least MinCanoeTripPercentage percent of the total trips should be by canoe. Additionally, at least MinDucksToShore ducks need to be taken to shore."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 5e52a405-731b-42f4-9897-e86786c2bbf7
encoding: FLOAT32
metadata:
{"key": "143", "chroma:document": "A soda company sends bottles of their soda to stores around the city in old and new vans. An old van can take CapacityOldVan soda bottles while a new van can take CapacityNewVan soda bottles. An old van produces PollutionOldVan units of pollution while a new van only produces PollutionNewVan units of pollution. The company needs to send at least MinBottles bottles. In addition, at most MaxNewVans new vans can be used. How many of each van should be used to minimize the total amount of pollution produced?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 6d92e777-e450-410a-8b5c-2b7a5dfbab89
encoding: FLOAT32
metadata:
{"key": "144", "chroma:document": "A lawn mowing service provides neighborhood services using small teams and large teams. A small team requires EmployeesPerSmallTeam employees and can mow AreaSmallTeam sq ft of lawn. A large team requires EmployeesPerLargeTeam employees and can mow AreaLargeTeam sq ft of lawn. The company has TotalEmployees employees available. The number of small teams must be at least SmallTeamsFactor times the number of large teams. There must be at least MinLargeTeams large teams and at least MinSmallTeams small teams. How many of each team type should be used to maximize the amount of lawn that can be mowed?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 6b4e804a-31ef-4ecf-aadd-82ce613d2776
encoding: FLOAT32
metadata:
{"key": "145", "chroma:document": "An aquarium conducts shows using otters and dolphins. Each otter performs OtterTricks tricks and requires OtterTreats treats to do so. Each dolphin performs DolphinTricks trick and requires DolphinTreats treats to do so. Considering the popularity, at least MinDolphins dolphins must be used, and no more than MaxOtterPercentage of the performers can be otters. With a total of TotalTreats treats available, the task is to maximize the total number of tricks that can be performed."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: b834e92c-7d1a-482e-a707-0e4d243845d4
encoding: FLOAT32
metadata:
{"key": "147", "chroma:document": "An oil and gas company is sending their oil to the port using containers and trucks. A container can hold ContainerCapacity units of oil while a truck can hold TruckCapacity units of oil. Due to government restrictions, the number of trucks used has to be at most MaxTruckContainerRatio times the number of containers used. If at least MinOilRequired units of oil need to be sent to the port and at least MinContainers containers need to be used, the objective is to minimize the total number of containers and trucks used."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 84c723d1-3b81-4adf-9709-0abbd3c2d67c
encoding: FLOAT32
metadata:
{"key": "148", "chroma:document": "A school is organizing a field trip and plans to hire buses of two types. One type of bus has a capacity of SmallBusCapacity students, and the other type has a capacity of LargeBusCapacity students. The school needs to provide transportation for at least MinStudents students. In addition, no more than a fraction MaxLargeBusPercentage of the total number of hired buses can be large buses. The objective is to determine the number of each type of bus to hire to minimize the total number of buses."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 71af57bb-d7bd-4e1b-b84b-74f126fc3205
encoding: FLOAT32
metadata:
{"key": "149", "chroma:document": "A meat shop ships their burger patties using refrigerated trucks and vans. Each truck can take TruckCapacity patties at a cost of TruckCost per trip. Each van can take VanCapacity patties at a cost of VanCost per trip. The number of trucks must not exceed the number of vans. The meat shop has to ship at least MinPatties patties and they have a maximum budget of MaxBudget. How should they plan their shipment to minimize the total number of trips?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 8db7c57e-03d3-45e1-9dfb-f7a9202fdfab
encoding: FLOAT32
metadata:
{"key": "150", "chroma:document": "A florist transports his flowers to stores in small bouquets and large bouquets. Each small bouquet has SmallBouquetFlowers flowers while each large bouquet has LargeBouquetFlowers flowers. The florist can transport at most MaxSmallBouquets small bouquets and MaxLargeBouquets large bouquets. In total, he can transport at most MaxTotalBouquets bouquets, and he must transport at least MinLargeBouquets large bouquets. Additionally, he must transport at least SmallLargeRatio times the number of large bouquets as small bouquets. The goal is to determine the number of each bouquet type he should transport to maximize the total number of flowers that reach the stores."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 0854929f-cbab-4335-a8b3-13291411bcd0
encoding: FLOAT32
metadata:
{"key": "151", "chroma:document": "A toy store decides to deliver gifts using two shipping companies: a new company and an old company. The new company can deliver NewCompanyGiftCapacity gifts per trip, while the old company can deliver OldCompanyGiftCapacity gifts per trip. The new company uses NewCompanyDieselUsage liters of diesel per trip, while the old company uses OldCompanyDieselUsage liters of diesel per trip. The toy store needs to deliver at least MinGiftsRequired gifts. The new company can make at most MaxNewCompanyTrips trips. To ensure the old company does not go out of business, at least MinOldCompanyTripPercentage of all trips must be made by the old company. The goal is to determine how many trips each company should make to minimize the total amount of diesel used."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: a7ada3aa-fce2-4e11-9f77-d7156a444d65
encoding: FLOAT32
metadata:
{"key": "152", "chroma:document": "A zoo needs to transport TotalMonkeys to the vet either by bus or by car. A bus can transport MonkeysPerBusTrip per trip and takes TimePerBusTrip. A car can transport MonkeysPerCarTrip per trip and takes TimePerCarTrip. There can be at most MaxBusTrips. In addition, since the monkeys get aggressive when there are too many in one place, at least MinCarTripPercentage of the trips should be by car. If the zoo needs to transport TotalMonkeys, how many trips of each should be done to minimize the total time required to transport the monkeys?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: d207107e-f7c9-4b9c-b83d-7f07e8ff06ac
encoding: FLOAT32
metadata:
{"key": "153", "chroma:document": "A farmer decides to move NumCows to a nearby farm using helicopters and trucks. A helicopter can take HelicopterCapacity cows per trip and creates HelicopterPollution units of pollution. A truck can take TruckCapacity cows per trip and creates TruckPollution units of pollution. The farmer only has enough money for at most MaxTruckTrips truck trips. The objective is to minimize the total amount of pollution produced while transporting NumCows."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: bc97d5da-b1bc-4862-ac58-8ceb8b287e36
encoding: FLOAT32
metadata:
{"key": "155", "chroma:document": "A meal service company delivers meals to customers either on electric bikes or scooters. A bike can hold MealsPerBike meals and requires ChargePerBike units of charge. A scooter can hold MealsPerScooter meals and requires ChargePerScooter units of charge. Since the city is more friendly towards scooters, at most MaxPercentageBikes percentage of the electric vehicles can be bikes and at least MinScooters scooters must be used. If the company only has TotalCharge units of charge available, how many of each vehicle should be used to maximize the number of meals that can be delivered?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 8ebb6e3c-cf34-4982-9c1f-407c3f20c910
encoding: FLOAT32
metadata:
{"key": "156", "chroma:document": "A car manufacturer ships their cars on large and small planes. A large plane can carry CarsPerLargePlane cars while a small plane can carry CarsPerSmallPlane cars. To reduce pollution, the number of large planes must be less than the number of small planes. The manufacturer wants to deliver at least TotalCars cars while minimizing the total number of planes used."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 1699018e-40d2-43ea-b18c-b0ed39dea84d
encoding: FLOAT32
metadata:
{"key": "157", "chroma:document": "A mine sends ore to the surface in small and large wagons. A small wagon holds SmallWagonCapacity units of ore while a large wagon holds LargeWagonCapacity units of ore. To avoid taking up too much space on the ramps, the number of small wagons must be at least MinRatioSmallToLarge times the number of large wagons. In addition, at least MinLargeWagons large wagons must be used. If TotalOre units of ore need to be taken to the surface, minimize the total number of wagons needed."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 21f906f6-959d-412f-8e2e-f1bb82532e25
encoding: FLOAT32
metadata:
{"key": "158", "chroma:document": "A theme park transports its visitors around the park either by scooter or rickshaw. A scooter can carry ScooterCapacity people while a rickshaw can carry RickshawCapacity people. To avoid excessive pollution, at most MaxRickshawProportion of the vehicles used can be rickshaws. If the park needs to transport at least MinVisitors visitors, minimize the total number of scooters used."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 0de01c2b-fee6-418e-9b4c-a634e92bb22e
encoding: FLOAT32
metadata:
{"key": "159", "chroma:document": "A company delivers their packages using two types of animals. One type of animal can carry PackagesPerCamel packages and requires FoodPerCamel units of food. The other type of animal can carry PackagesPerHorse packages and requires FoodPerHorse units of food. The company needs to deliver at least MinPackages packages and has TotalFood units of food available. Additionally, the number of the second type of animal cannot exceed the number of the first type of animal. The goal is to determine how many of each animal to use in order to minimize the total number of animals."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: c0842e88-7c2f-43d2-b84c-a0fc1ab8ef1b
encoding: FLOAT32
metadata:
{"key": "161", "chroma:document": "A mail delivery service in an island village delivers mail by regular and speed boats. A regular boat can carry MailCapacityRegular pieces of mail per trip and uses GasUsageRegular liters of gas. A speed boat can carry MailCapacitySpeed pieces of mail per trip and uses GasUsageSpeed liters of gas. There can be at most MaxRegularTrips regular boat trips. Since customers want their mail as fast as possible, at least MinSpeedBoatTripPercentage percent of the trips must be made by speed boats. If the service needs to deliver TotalMail pieces of mail, how many trips of each should be made to minimize the total amount of gas consumed?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 21b76544-c953-4862-ba77-6cfa42c24ed4
encoding: FLOAT32
metadata:
{"key": "162", "chroma:document": "A chicken farmer needs to transport TotalChicken using either buses or cars. A bus can carry BusCapacity and takes BusTimePerTrip hours per trip. A car can carry CarCapacity and takes CarTimePerTrip hours per trip. There can be at most MaxBusTrips and at least MinCarTripPercentage of the trips must be by car. The farmer needs to determine the number of trips by car and bus to minimize the total transportation time."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 22c611b3-8ce5-49ea-a628-088358f54acf
encoding: FLOAT32
metadata:
{"key": "163", "chroma:document": "Children can go to school either by van or by minibus. A van can take VanCapacity kids and produces VanPollution units of pollution. A minibus can take MinibusCapacity kids and produces MinibusPollution units of pollution. There are at least NumChildren kids that need to go to school and at most MaxMinibuses minibuses can be used. In addition, the number of vans used must exceed the number of minibuses."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: e131a77b-27c3-47d2-a652-ed0858ff260f
encoding: FLOAT32
metadata:
{"key": "167", "chroma:document": "A farmer needs to send at least MinCornWeight of corn to the city using either tractors or cars. A tractor can carry TractorCapacity of corn, and a car can carry CarCapacity of corn. The number of cars used has to be at least CarToTractorRatio times the number of tractors used. The objective is to minimize the total number of tractors and cars needed."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 7ccbf30a-f1c0-4ea4-95e8-14f7aadae795
encoding: FLOAT32
metadata:
{"key": "168", "chroma:document": "A village provides bike and car transportation for everyone. A bike can take PeoplePerBike people while a car can take PeoplePerCar people. Since cars are more expensive, at most MaxPercentageCars of the vehicles can be cars. If the village needs to transport at least MinPeople people, how many of each vehicle should be used to minimize the total number of bikes needed?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: cacbff12-335c-46f4-8814-28e1085a6903
encoding: FLOAT32
metadata:
{"key": "170", "chroma:document": "A water salesman collects water from a glacier and transports it in either small or large kegs. A small keg can hold SmallKegCapacity liters of water while a large keg can hold LargeKegCapacity liters of water. The salesman has available at most MaxSmallKegs small kegs and MaxLargeKegs large kegs. Since small kegs are easier to carry, at least MinSmallToLargeRatio small kegs must be used for every large keg. If he can transport at most MaxTotalKegs kegs total and at least MinLargeKegs kegs must be large, how many of each should he use to maximize the total amount of glacial water he can transport?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 8852b644-3d92-4566-9428-0cd96e6b7f94
encoding: FLOAT32
metadata:
{"key": "171", "chroma:document": "A city needs to transport at least TotalMail pieces of mail using either submarines or boats. A submarine can carry SubmarineCapacity pieces of mail per trip and uses SubmarineGasUsage liters of gas per trip. A boat can carry BoatCapacity pieces of mail per trip and uses BoatGasUsage liters of gas per trip. The maximum allowable trips by submarine is MaxSubmarineTrips. At least MinBoatTripPercentage of the trips must be made by boat. The objective is to determine the number of submarine trips and boat trips that minimize the total gas usage while meeting these constraints."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: fa19b5b0-766c-4313-8751-44736d82f111
encoding: FLOAT32
metadata:
{"key": "172", "chroma:document": "The weather is freezing and the fish in the pond need to be transported either by helicopter or car. A helicopter can take HelicopterFishCapacity fish per trip and takes HelicopterTripTime minutes. A car can take CarFishCapacity fish per trip and takes CarTripTime minutes. Since helicopter trips are expensive, there can be at most MaxHelicopterTrips helicopter trips. In addition, at least MinCarTripPercentage of the trips should be by car. If at least MinFishRequired fish need to be transported, how many of each trip should be taken to minimize the total time needed?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: ab5e33bc-93eb-4690-a9e2-3a070ee98084
encoding: FLOAT32
metadata:
{"key": "173", "chroma:document": "A tourist spot in the mountains allows visitors to travel to the top either by hot-air balloon or gondola lift. A hot air balloon can carry BalloonCapacity visitors while a gondola lift can carry GondolaCapacity visitors. Each hot air balloon produces BalloonPollution units of pollution while each gondola lift produces GondolaPollution units of pollution. There can be at most MaxBalloons hot-air balloon rides and at least MinVisitors visitors need to be transported. How many of each type of transport method should be taken to minimize the total pollution produced?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: de247327-65c9-4cbe-9783-088f533daba6
encoding: FLOAT32
metadata:
{"key": "174", "chroma:document": "A factory transports rice to the city in horse-drawn carts that are either medium or large size. A medium sized cart requires HorsesPerMediumCart horses and can carry CapacityMediumCart kg of rice. A large sized cart requires HorsesPerLargeCart horses and can carry CapacityLargeCart kg of rice. The factory has NumHorses horses available. The number of medium sized carts must be MediumToLargeCartRatio times the number of large sized carts. There must be at least MinMediumCarts medium sized carts and at least MinLargeCarts large sized carts. How many of each cart size should be used to maximize the amount of rice that can be transported?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 0f261420-f608-482c-a360-da456e4afab1
encoding: FLOAT32
metadata:
{"key": "175", "chroma:document": "A dog school trains labradors and golden retrievers to deliver newspapers. A labrador can deliver NewspapersPerLabrador newspapers at a time and requires TreatsPerLabrador small bone treats for service. A golden retriever can deliver NewspapersPerGoldenRetriever newspapers at a time and requires TreatsPerGoldenRetriever small bone treats per service. The school only has TotalTreats small bone treats available. In addition, at least MinGoldenRetrievers golden retrievers must be used and at most MaxLabradorPercentage of the dogs can be labradors. How many of each dog should be used to maximize the number of newspapers that can be delivered?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: cfbbbfb7-02d2-4aa0-8926-c436a0982e53
encoding: FLOAT32
metadata:
{"key": "176", "chroma:document": "A construction company in the tropics uses cows and elephants to carry bricks. A cow can carry BricksPerCow on its back while an elephant can carry BricksPerElephant on its back. To avoid having elephants create too much traffic, the number of elephants cannot exceed the number of cows. In addition, there can be at most MaxCowsToElephantsRatio times the number of cows as elephants (i.e., the maximum ratio of cows to elephants is MaxCowsToElephantsRatio). If the company needs to transport at least MinBricks, find the minimum number of animals, cows and elephants, that can be used."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 21bf2927-b303-473a-abc5-ed7f5f4c9656
encoding: FLOAT32
metadata:
{"key": "177", "chroma:document": "A farmer on an island sends corn to the main land either by ferry or light rail. Each ferry trip can take FerryCapacity boxes of corn while each light rail trip can take LightRailCapacity boxes of corn. Since ferry trips are slow, the number of light rail trip has to be at least LightRailToFerryRatio times the number of ferry trips. If the farmer wants to send at least MinBoxes boxes of corn, minimize the total number of trips of either type needed."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 7c0cc650-48f6-4a6c-8b12-2875a19f28a7
encoding: FLOAT32
metadata:
{"key": "179", "chroma:document": "A chemical company is transporting their hydrogen using two different methods, high pressure tube trailers and liquefied hydrogen tankers. Constants: VolumeHPTT is the volume transported per high pressure tube trailer trip. CostHPTT is the cost per high pressure tube trailer trip. VolumeLHT is the volume transported per liquefied hydrogen tanker trip. CostLHT is the cost per liquefied hydrogen tanker trip. MinVolume is the minimum volume of hydrogen to transport. Budget is the budget available for transportation. Decision Variables: NumHPTT is the number of trips done using the high-pressure tube trailers, and NumLHT is the number of trips done using the liquefied hydrogen tankers. Constraints: The total transported volume (VolumeHPTT * NumHPTT + VolumeLHT * NumLHT) must be at least MinVolume. The total cost (CostHPTT * NumHPTT + CostLHT * NumLHT) must not exceed Budget. The number of high pressure tube trailer trips (NumHPTT) must be less than the number of liquefied hydrogen tanker trips (NumLHT). Objective: Minimize the total number of trips (NumHPTT + NumLHT)."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: ce3a7e6f-85f1-4677-9bcf-00bd9eebc7db
encoding: FLOAT32
metadata:
{"key": "180", "chroma:document": "A farmer transports his grapes in either small crates or large crates. Each small crate can take SmallCrateCapacity number of grapes while each large crate can take LargeCrateCapacity number of grapes. The customers prefer smaller crates, so the farmer must use at least MinSmallCratesToLargeCratesRatio times as many small crates as large crates. The farmer has at most MaxSmallCrates small crates and at most MaxLargeCrates large crates available. His truck can transport at most MaxTotalCrates crates in total, using at least MinLargeCrates large crates. The objective is to determine the number of small and large crates to maximize the total number of grapes transported."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: aa524aba-997c-4638-9a22-0f1a9ab07530
encoding: FLOAT32
metadata:
{"key": "182", "chroma:document": "Patients need to be transported to the hospital by either a helicopter or a bus. A helicopter can transport HelicopterCapacity patients per trip and takes HelicopterTripTime hours. A bus can transport BusCapacity patients per trip and takes BusTripTime hours. At least MinPatientsToTransport patients need to be transported and at least MinHelicopterTripPercentage percent of the trips should be by helicopter. Additionally, there can be at most MaxBusTrips bus trips. The objective is to minimize the total time to transport the patients."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: a819cf62-ffe0-4c72-b586-f4759f537862
encoding: FLOAT32
metadata:
{"key": "183", "chroma:document": "Employees have the option of car-pooling to work or taking the company bus. A car can take CarCapacity employees and produces CarPollution units of pollution, while a bus can take BusCapacity employees and produces BusPollution units of pollution. At least NumEmployees employees need to be transported and a maximum of MaxBuses buses can be used. How many of each type of transport should be taken to minimize the total pollution produced."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 738bba71-5942-4704-9500-f664e38a07dd
encoding: FLOAT32
metadata:
{"key": "184", "chroma:document": "A company removes snow using two types of trucks: small trucks and large trucks. Let NumSmallTrucks represent the number of small trucks and NumLargeTrucks represent the number of large trucks. A small truck requires PeopleForSmallTruck people to shovel the snow and can carry CapacitySmallTruck units of snow. A large truck requires PeopleForLargeTruck people to shovel the snow and can carry CapacityLargeTruck units of snow. The company has a total of TotalPeople available. At least MinSmallTrucks small trucks are required. At least MinLargeTrucks large trucks are required. Additionally, the number of small trucks (NumSmallTrucks) must be twice the number of large trucks (NumLargeTrucks). The goal is to determine the number of each type of truck to use in order to maximize the total amount of snow transported."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: ab2ec589-3ad4-4897-8062-77f83ec39a90
encoding: FLOAT32
metadata:
{"key": "185", "chroma:document": "A magic school sends letters to students either by carrier pigeons or owls. A carrier pigeon can carry CarrierPigeonCapacity letters at a time and requires CarrierPigeonTreats treats for service. An owl can carry OwlCapacity letters at a time and requires OwlTreats treats for service. At most MaxOwlPercentage of the birds can be owls. In addition, the school only has NumTreats treats available and at least MinCarrierPigeons carrier pigeons must be used. How many of each bird can be used to maximize the total number of letters that can be sent."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: cc60b0f5-fd7a-40a5-a594-21934c16a1cc
encoding: FLOAT32
metadata:
{"key": "187", "chroma:document": "A large fishing boat sends fish back to shore either by small canoes or smaller diesel boats. A small canoe can carry back CapacityCanoe fish while a small diesel boat can carry back CapacityDieselBoat fish. In order to follow environmental rules, the number of small canoes used has to be at least CanoeToDieselRatio times the number of diesel boats used. If at least MinFish fish need to be transported to shore, minimize the total number of canoes and diesel boats needed."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 474fd60e-6d3c-4d41-acc4-4f2c4e9bafea
encoding: FLOAT32
metadata:
{"key": "189", "chroma:document": "A company needs to provide a diet that meets at least MinCalories calories, MinProtein grams of protein, and MinCarbs grams of carbs for its workers. One type of food, referred to as a hamburger, costs HamburgerCost and contains HamburgerCalories calories, HamburgerProtein grams of protein, and HamburgerCarbs grams of carbs. Another type of food, referred to as a chicken wrap, costs ChickenWrapCost and contains ChickenWrapCalories calories, ChickenWrapProtein grams of protein, and ChickenWrapCarbs grams of carbs. The objective is to find the minimum cost combination of these foods that meets the dietary requirements."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 60ae6f40-bf83-42fd-9f8d-bfac72ff6bd0
encoding: FLOAT32
metadata:
{"key": "192", "chroma:document": "A company makes NumProducts different products. Each product i requires AssemblyTime[i] of assembly and SandingTime[i] of sanding. The company has available AvailableAssemblyTime for assembly and AvailableSandingTime for sanding. The profit per unit of product i is Profit[i]. How many of each product should the company make to maximize profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 85efb4f3-e630-4ded-87b3-b4c3d54a345b
encoding: FLOAT32
metadata:
{"key": "194", "chroma:document": "A young boy wants to get a minimum of MinCalcium units of calcium and MinIron units of iron per day. A glass of milk costs CostMilk and contains CalciumMilk units of calcium and IronMilk units of iron. A plate of vegetables costs CostVegetables and contains CalciumVegetables units of calcium and IronVegetables units of iron. The goal is to determine the number of glasses of milk and plates of vegetables he should consume to minimize his cost."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 984812c4-ce67-4944-99c1-3a331a43a3c7
encoding: FLOAT32
metadata:
{"key": "195", "chroma:document": "Bob wants to design a diet consisting of two types of food items. Assume that the first food item costs CostNoodles per serving and contains CaloriesNoodles calories and ProteinNoodles grams of protein. Assume that the second food item costs CostProteinBar per serving and contains CaloriesProteinBar calories and ProteinProteinBar grams of protein. Bob is interested in minimizing the cost of his diet while ensuring that his meals provide at least MinCalories calories and at least MinProtein grams of protein per day."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 77b0cdcb-5d4c-4184-b187-d6dad7f5635a
encoding: FLOAT32
metadata:
{"key": "202", "chroma:document": "An individual takes two different supplements to satisfy daily iron and calcium requirements. Each pill of the first supplement contains IronInSupplementA units of iron and CalciumInSupplementA units of calcium. Each pill of the second supplement contains IronInSupplementB units of iron and CalciumInSupplementB units of calcium. The individual needs at least MinIronRequirement units of iron and at least MinCalciumRequirement units of calcium per day. The cost per pill of the first supplement is PriceSupplementA, and the cost per pill of the second supplement is PriceSupplementB. The objective is to determine the number of pills of each supplement the individual should take to minimize the total cost while meeting the daily iron and calcium requirements."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 8dfa51bc-bcbb-46b5-bb56-aebcf52d7cfc
encoding: FLOAT32
metadata:
{"key": "204", "chroma:document": "A woman has TotalMoney to gamble on three sports bets: a basketball tournament, a horse race, and a soccer game. Based on simple analysis, the woman determines her chance of losing her money would be ProbLoseBasketball for the basketball tournament, ProbLoseHorseRace for the horse race, and ProbLoseSoccer for the soccer game. The payout for each dollar put on each bet will be PayoutBasketball for the basketball tournament, PayoutHorseRace for the horse race, and PayoutSoccer for the soccer game. She limits her average chance of losing her money to at most MaxAvgProbLose. The goal is to determine the amount of money to put on each sport bet to maximize her expected payout."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: e3529762-def7-4a19-9653-16b2681c6f61
encoding: FLOAT32
metadata:
{"key": "205", "chroma:document": "A repairman fixes two types of appliances. Each appliance of the first type (washing machine) takes InspectionTimeWashingMachine for inspection and FixingTimeWashingMachine for fixing. Each appliance of the second type (freezer) takes InspectionTimeFreezer for inspection and FixingTimeFreezer for fixing. The repairman has AvailableInspectionTime for inspection and AvailableFixingTime in his schedule. If each appliance of the first type repaired earns him EarningWashingMachine and each appliance of the second type repaired earns him EarningFreezer, how many of each appliance should he fix to maximize his earnings?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 026ba70f-75c1-428a-80ec-47539a887e1c
encoding: FLOAT32
metadata:
{"key": "206", "chroma:document": "A bakery has TotalBatter of batter and TotalMilk of milk to make their crepe cakes, sponge cakes, and birthday cakes. A crepe cake needs BatterCrepeCake of batter and MilkCrepeCake of milk. A sponge cake requires BatterSpongeCake of batter and MilkSpongeCake of milk. A birthday cake requires BatterBirthdayCake of batter and MilkBirthdayCake of milk. If the profit per crepe cake is ProfitCrepeCake, the profit per sponge cake is ProfitSpongeCake, and the profit per birthday cake is ProfitBirthdayCake, how many of each should the bakery make to maximize their profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 893aebd2-8f0f-4611-b8b3-2056f3e25488
encoding: FLOAT32
metadata:
{"key": "207", "chroma:document": "Super Shop sells two types of snacks in bulk: cat paw snacks and gold shark snacks. It plans to create two mix products. The first mix contains PercentCatPawFirstMix of cat paw snacks and PercentGoldSharkFirstMix of gold shark snacks. The second mix contains PercentCatPawSecondMix of cat paw snacks and PercentGoldSharkSecondMix of gold shark snacks. The store has AvailableCatPawSnacks of cat paw snacks and AvailableGoldSharkSnacks of gold shark snacks on hand. The profit per kilogram of the first mix is ProfitFirstMix and the profit per kilogram of the second mix is ProfitSecondMix. The objective is to determine how many kilograms of each mix should be prepared to maximize profit."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: a1d07385-43e0-4400-83a6-3c1322d7a45e
encoding: FLOAT32
metadata:
{"key": "211", "chroma:document": "A company sells two types of subscription software packages: a personal license and a commercial license which will cost CostPersonalLicense and CostCommercialLicense to generate respectively. The marketing department estimates that they can sell at most MaxLicenses licenses for both versions combined a month. The profit per personal license is ProfitPersonalLicense and the profit per commercial license is ProfitCommercialLicense. If the company does not want to spend more than BudgetLimit, how many of each software package should they produce to maximize the profits."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 287eafcd-00c4-496d-b300-db5cdc174aa0
encoding: FLOAT32
metadata:
{"key": "215", "chroma:document": "The government is reworking pipes to transport water to houses. Water can be transported through wide pipes or narrow pipes. Wide pipes transport WidePipeFlowRate units of water per minute, and narrow pipes transport NarrowPipeFlowRate units of water per minute. The number of wide pipes can be at most WidePipeFraction the number of narrow pipes. There needs to be at least MinWaterTransport units of water transported every minute, and at least MinWidePipes wide pipes must be used. Minimize the total number of pipes required."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 70781d26-b900-45b9-8943-61e7ffe1bd7c
encoding: FLOAT32
metadata:
{"key": "220", "chroma:document": "A student takes pills, where each pill type has a different effectiveness time. The student must take at least TotalPills pills over a month, with at least MinVitaminDPills of them being vitamin D pills. The effectiveness times for calcium and vitamin D pills are CalciumTime and VitaminDTime respectively. The student must also take more calcium pills than vitamin D pills. The goal is to determine the number of each type of pill to take in order to minimize the total effectiveness time sum of all pills taken."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 9fa852f4-04b7-4451-a983-df1aa3a14561
encoding: FLOAT32
metadata:
{"key": "221", "chroma:document": "An amusement park has two types of games: throwing and climbing games. Throwing games attract ThrowingGameCustomers customers every hour and climbing games attract ClimbingGameCustomers customers every hour. Throwing games cost the amusement park ThrowingGameCost in prizes per hour whereas climbing games cost ClimbingGameCost in prizes per hour. Since throwing games yield the most profit, there must be at least ThrowingToClimbingRatio times as many throwing games as climbing games. However, at least MinClimbingGames games must be climbing games. If the amusement park can have at most MaxPrizeCost in prizes every hour, maximize the total number of customers attracted every hour."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 80033f66-ef95-4961-9c82-ee2e42fef187
encoding: FLOAT32
metadata:
{"key": "222", "chroma:document": "Determine the quantity of circular and rectangular tables to set up at a science fair in order to maximize the number of catered guests. Each circular table fits PosterBoardsCircular poster boards and ParticipantsCircular participants, catering to GuestsCircular guests and taking up SpaceCircularTable units of space. Each rectangular table fits PosterBoardsRectangular poster boards and ParticipantsRectangular participants, catering to GuestsRectangular guests and taking up SpaceRectangularTable units of space. The fair must accommodate at least MinParticipants participants and MinPosterBoards poster boards, without exceeding the TotalAvailableSpace units of space."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 8e0171a3-273a-46aa-bdd7-dca431227ab2
encoding: FLOAT32
metadata:
{"key": "223", "chroma:document": "An oil and gas company has two types of pipes, a high-volume and a low-volume one. Every day, the high-volume pipe allows a throughput of HighVolumePipeThroughput and it is recommended that TechniciansPerHighVolumePipe technicians closely monitor the pipes to ensure that it is functioning properly. Each day, the low-volume pipe allows a throughput of LowVolumePipeThroughput and TechniciansPerLowVolumePipe technicians should closely monitor for safety reasons. Every day, the oil and gas company needs to meet the demands of at least MinimumDailyDemand of gas and they have TotalTechnicians technicians on their staff. Since the high-volume pipe has a higher risk of environmental damage, at most MaxHighVolumePipePercentage of the total number of pipes can be high-volume ones. Additionally, there must be a minimum of MinLowVolumePipes low-volume pipes. How many of each pipe types should be used to reduce the total number of pipes required?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 3a56a320-6d64-4e09-85c7-c0b33c39f1fd
encoding: FLOAT32
metadata:
{"key": "224", "chroma:document": "A hospital hires workers to provide ultrasound services. An ultrasound technician works TechnicianHoursPerShift hours per shift and is paid TechnicianPaymentPerShift per shift, while a graduate researcher works ResearcherHoursPerShift hours per shift and is paid ResearcherPaymentPerShift per shift. Due to regulations, there must be TechnicianToResearcherRatio times as many ultrasound technician shifts as graduate researcher shifts. The hospital requires TotalRequiredHours of ultrasound services and has a TotalBudget available. The objective is to schedule the minimum total number of workers."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 20b4ad85-123a-4eb1-98cc-6ead524d9078
encoding: FLOAT32
metadata:
{"key": "226", "chroma:document": "A delivery person can have shifts on either bikes or scooters. A shift on a bike delivers OrdersPerBikeShift orders, uses EnergyPerBikeShift units of energy, and brings in TipsPerBikeShift in tips because it is faster. A shift on a scooter delivers OrdersPerScooterShift orders, uses EnergyPerScooterShift units of energy, and brings in TipsPerScooterShift in tips. The delivery person has a total of TotalShifts available per month and TotalEnergy units of energy and must deliver at least MinOrders orders. Additionally, they must have at least MinScooterShifts shifts on scooters because bikes are harder to get. The goal is to determine the number of shifts on each type of transportation to maximize the tips received."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: a508c25f-8f86-4771-8066-68d8d1f60269
encoding: FLOAT32
metadata:
{"key": "227", "chroma:document": "A singer can hold two types of concerts: pop and R&B. Each pop concert brings in PopAudience audience members and requires PopPracticeDays practice days. Each R&B concert brings in RnBAudience audience members and requires RnBPracticeDays practice days. The singer must bring in at least MinAudienceRequired total audience members and has a maximum of MaxPracticeDays practice days available. Additionally, the singer can perform at most MaxRnBConcertRate of his total concerts as R&B concerts. The objective is to determine the number of each type of concert to minimize the total number of concerts."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: b83a9ce1-c16a-4334-9bb8-742f9bfd39bb
encoding: FLOAT32
metadata:
{"key": "228", "chroma:document": "A neighbourhood pizza restaurant sells two sizes of pizzas: large and medium. Each large pizza requires DoughLargePizza units of dough and ToppingsLargePizza units of toppings, and takes TimeLargePizza minutes to bake. Each medium pizza requires DoughMediumPizza units of dough and ToppingsMediumPizza units of toppings, and takes TimeMediumPizza minutes to bake. The restaurant must use at least MinDough units of dough and at least MinToppings units of toppings. Due to a promotion, at least MinMediumPizza medium pizzas need to be made. To cater to regulars, the number of large pizzas should be at least LargeToMediumRatio times the number of medium pizzas, where LargeToMediumRatio represents the value 2. The objective is to minimize the total baking time."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 26dadc35-30e5-4cbd-a653-08972b24a0f4
encoding: FLOAT32
metadata:
{"key": "231", "chroma:document": "A restaurant can deliver their food by two methods. Servers can deliver by one method and will have CartInteractions customer interactions and will need to refill food CartRefills times per hour. They can also deliver food by another method with increased mobility, achieving HandInteractions customer interactions while needing HandRefills refills per hour. At least MinCartPercentage of delivery shifts must be by the first method. Additionally, there must be at least MinHandServers servers delivering by the second method. The restaurant aims to have TotalInteractions customer interactions per hour. Determine the number of servers for each delivery method to minimize the total number of refills per hour."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: cbcc433c-0e11-48fd-8783-69897a249ddb
encoding: FLOAT32
metadata:
{"key": "233", "chroma:document": "A restaurant has two combos available to their customers: an original meal and an experimental meal. The original meal generates OriginalFoodWaste units of food waste, OriginalWrappingWaste units of wrapping waste, and takes OriginalCookingTime minutes to cook. The experimental meal generates ExperimentalFoodWaste units of food waste, ExperimentalWrappingWaste units of wrapping waste, and takes ExperimentalCookingTime minutes to cook. The restaurant must adhere to a maximum of MaxWrappingWaste units of wrapping waste and MaxFoodWaste units of food waste as regulated by the government. The goal is to determine the number of each meal to be promoted by the waiting staff to minimize the total cooking time while complying with waste constraints."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 046ede13-827b-42ce-9653-b9da94d3dc08
encoding: FLOAT32
metadata:
{"key": "234", "chroma:document": "A metal-working shop has access to two types of metal-working equipment, a chop saw and a steel cutter. A chop saw can work ChopSawCapacity of metal and generates ChopSawWaste units of waste every day. A steel cutter can work SteelCutterCapacity of metal and generates SteelCutterWaste units of waste every day. The metal-working shop must cut TotalMetalCuttingRequirement of metal every day. However, there is a waste limitation and they may at most produce MaxAllowedWaste units of waste every day. The objective is to minimize the total number of metal-working equipment needed."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: c8d89928-35c4-428f-8039-e24c169a2d05
encoding: FLOAT32
metadata:
{"key": "237", "chroma:document": "A market owner wants to start a jam business. He can either sell one unit of jam to customers in a set of small packets or jugs. A set of small packets can hold VolumeSmallPackets ml of jam while a jug can hold VolumeJug ml of jam. Since a set of small packets are more expensive to make, at least MinRatioJugToPackets times the number of jugs must be used as sets of small packets. Additionally, at least MinSetsSmallPackets sets of small packets should be filled. If the market owner has TotalVolumeJam ml of jam, how many sets of small packets or jugs should be selected to maximize the total number of units that he can sell to his customers?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 5f30af58-f05a-4f45-aafd-7918a13563f6
encoding: FLOAT32
metadata:
{"key": "238", "chroma:document": "The goal is to determine the quantities of two types of meals, one denoted as 'salad' and the other as 'fruit bowl.' Each type of meal contributes different amounts of vitamins, fibres, and potassium. The objective is to maximize the total potassium intake. There are constraints to ensure a minimum required intake of vitamins and fibres: MinVitamin and MinFibre. Each salad provides VitaminPerSalad units of vitamins and FibrePerSalad units of fibre. Each fruit bowl provides VitaminPerFruitBowl units of vitamins and FibrePerFruitBowl units of fibre. Additionally, there is a constraint that at most MaxFruitBowlPercentage of the meals can be fruit bowls. Each salad contains PotassiumPerSalad units of potassium and each fruit bowl contains PotassiumPerFruitBowl units of potassium."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: f4fda0f7-008d-4267-85ae-4b81c09f42a5
encoding: FLOAT32
metadata:
{"key": "239", "chroma:document": "A company wants to determine the number of retail stores and factory outlets to open to satisfy MinCustomersPerDay, while using at most MaxEmployees. Each retail store brings in RetailStoreCustomers and requires RetailStoreEmployees to operate. Each factory outlet brings in FactoryOutletCustomers and requires FactoryOutletEmployees to run. The goal is to minimize the number of retail stores and factory outlets that need to be open."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 8f3ada7a-032a-4e85-9df8-96f0588aa8fc
encoding: FLOAT32
metadata:
{"key": "240", "chroma:document": "A soda company needs to bottle at least MinTotalVolume of soda every day. A can holds VolumeCan of soda whereas a bottle holds VolumeBottle of soda. The number of cans must be at least MinRatioCansToBottles times the number of glass bottles, and at least MinBottles glass bottles must be produced due to contracts. How many cans and bottles should be made to maximize the total number of units produced?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: e5403774-f3f6-4900-aad7-e0af23e7e1bb
encoding: FLOAT32
metadata:
{"key": "241", "chroma:document": "A candle-making company can move their inventory of candles using freight and air. Freight can transport TonsPerFreight tons per trip while using air can transport TonsPerAir tons per trip. Since freight takes longer, the cost for each freight trip is FreightCost while the cost over air for each trip is AirCost. The company needs to transport at least TotalTons tons of candles and they have a budget of Budget. Additionally, due to some urgent orders, at least MinAirPercentage of total tons must be transported through air. There must also be at least MinFreightTrips trips through freight. How many of trip by each should be scheduled to minimize the total number of trips?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 094c8245-ebe4-43a0-8b5d-872cc6e790d7
encoding: FLOAT32
metadata:
{"key": "242", "chroma:document": "A production company needs to transport TotalPeople using large mobile production units or small mobile production units. Large mobile production units can hold LargeUnitCapacity people and take up LargeUnitParkingSpots parking spots whereas small mobile production units can hold SmallUnitCapacity people and take up SmallUnitParkingSpots parking spots. Movie stars prefer to have their small mobile production unit to share with a close staff, therefore at least MinSmallUnits units must be small mobile units. However, due to logistic limitations, large mobile production units are more space efficient per spot, they must make up at least MinPercentageLargeUnits of all vehicles. Minimize the total number of parking spots required by this production."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: da93b97c-393e-49be-95c4-fc2b43cc5c73
encoding: FLOAT32
metadata:
{"key": "243", "chroma:document": "A company ships items to stores using two different types of boxes. A small box holds MasksInSmallBox masks whereas a large box holds MasksInLargeBox masks. Since small boxes are easier to stack and will be used first to stock stores, there must be at least MinSmallToLargeRatio times as many small boxes as large boxes. Additionally, at least MinLargeBoxes large boxes must be used. If at least MinMasksRequired masks are required to be distributed, how many of each size of box should be used to minimize the total number of boxes needed?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 7634da32-859d-456e-977e-7ae906026284
encoding: FLOAT32
metadata:
{"key": "245", "chroma:document": "An autobody shop needs to purchase two types of car jacks, an automatic electric one, or a gas-powered one. The automatic electric one can process CarsPerHourElectric cars every hour and uses ElectricityPerHourElectric units of electricity whereas the gas-powered one can process CarsPerHourGas cars each hour using GasPerHourGas units of gas. Since there is a limit to how many automatic electric ones there can be due to the limited number of power outlets, the shop must use less than MaxElectricJacks automatic electric ones. The shop can use at most MaxElectricity units of electricity and MaxGas units of gas. How many of each type of jack should the shop purchase to maximize the amount of cars processed every hour?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 3054e54e-77c0-44fd-8814-b0dd92fceaa9
encoding: FLOAT32
metadata:
{"key": "246", "chroma:document": "A railway company is planning the infrastructure for the city and is considering two types of transportation, trains and trams. Each train can transport PeoplePerTrain people comfortably per hour and each tram can transport PeoplePerTram people comfortably per hour. Since trains take longer to build, the number of trams must be at least MinTramToTrainRatio times the number of trains. The company wants to transport at least MinTotalPeople people per hour and aims to minimize the total number of transportation units."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: b9a1b683-8b5b-4f8c-9903-d55cf5535e58
encoding: FLOAT32
metadata:
{"key": "247", "chroma:document": "An automotive company is comparing NumCatalysts different catalysts. The process with catalyst i requires PlatinumRequired[i] units of platinum and PalladiumRequired[i] units of palladium and can perform the conversion to carbon dioxide at a rate of ConversionRate[i] units per second. There are TotalPlatinumAvailable units of platinum and TotalPalladiumAvailable units of palladium available. How many of each catalyst should be used to maximize the amount converted into carbon dioxide?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: b3d10a50-50b2-4e36-8035-c8456055e202
encoding: FLOAT32
metadata:
{"key": "248", "chroma:document": "There are two processes, J and P, to extract metal from ores. Process J extracts MetalExtractedJ units of metal using WaterUsedJ units of water and produces PollutionProducedJ units of pollution. Process P extracts MetalExtractedP units of metal using WaterUsedP units of water and produces PollutionProducedP units of pollution. The objective is to determine the number of times each process should be performed to maximize the total metal extracted, subject to the constraints that the total water used does not exceed MaxWater units and the total pollution produced does not exceed MaxPollution units."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 12dc1009-7f2e-4c95-831f-ea034c188106
encoding: FLOAT32
metadata:
{"key": "249", "chroma:document": "An airport needs to install either escalators or elevators to transport people. Escalators have a transport capacity of EscalatorCapacity and take up EscalatorSpace units of space. Elevators have a transport capacity of ElevatorCapacity and take up ElevatorSpace units of space. The total transport capacity of all installed escalators and elevators must be at least RequiredCapacity. Additionally, the number of escalators must be at least EscalatorElevatorRatio times the number of elevators, and at least MinElevators elevators must be used. The goal is to minimize the total units of space taken by escalators and elevators."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: d4f35cd9-5669-4df3-a941-c5ac970ceb4a
encoding: FLOAT32
metadata:
{"key": "250", "chroma:document": "A research group is making fabric and plastic using two methods, method A and method B. Method A produces FabricUnitsA units of fabric and PlasticUnitsA units of plastic per hour. Method B produces FabricUnitsB units of fabric and PlasticUnitsB units of plastic per hour. Method A requires SpecialElementA units of a special element while method B requires SpecialElementB units of the same special element. The research group has available TotalSpecialElement units of the special element and must make at least MinFabric units of fabric and MinPlastic units of plastic. How many of each method should be executed to minimize the total time needed?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 8bed7e72-81bf-4fca-98c5-2f1a1631842c
encoding: FLOAT32
metadata:
{"key": "252", "chroma:document": "Due to an accident, at least MinLocals locals must be moved across a lake. They can either be transported over the lake by a kayak or a motorboat. Kayaks can transport KayakCapacity people per trip and motorboats can transport MotorboatCapacity people per trip. Kayaks take KayakTime minutes per trip whereas motorboats take MotorboatTime minutes per trip. Due to the limited number of motorboats available to the locals, there can be at most MaxMotorboatTrips motorboat trips and at least MinKayakTripProportion of the total trips should be by kayak. How many of each transportation method should be used to minimize the total amount of time needed to transport all the locals?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 4aa426db-ccc1-42a5-9bfd-3225bdb0b92b
encoding: FLOAT32
metadata:
{"key": "254", "chroma:document": "A researcher is outsourcing annotations and has two options: a specialized third-party or a common third-party annotation company. The specialized company can annotate at a rate of SpecializedRate images per hour whereas the common company can annotate at a rate of CommonRate images per hour. However, the specialized company charges SpecializedCost per hour and the common company charges CommonCost per hour. The researcher has deadlines to meet and must complete a dataset of at least TotalImages images. They also have some special images that only the specialized company can annotate. Therefore, at least a third of the TotalImages must be allocated to the specialized company."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 609f47d3-f752-4f6f-9176-d6c88bd13d41
encoding: FLOAT32
metadata:
{"key": "255", "chroma:document": "A golf course is organizing an event and can transport guests using either golf carts or pull carts. Each golf cart can transport GuestsPerGolfCart guests, while each pull cart can transport GuestsPerPullCart guest. However, due to spatial constraints, at most MaxGolfCartPercentage of all carts can be golf carts. The goal is to transport at least MinGuests guests while minimizing the total number of carts used."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 450ee288-4c59-484e-aa48-0908ff3dfedf
encoding: FLOAT32
metadata:
{"key": "256", "chroma:document": "A smoothie shop produces two different types of smoothies: acai berry smoothies and banana chocolate smoothies. It takes AcaiBerriesPerAcaiSmoothie units of acai berries and WaterPerAcaiSmoothie units of water to make one acai berry smoothie. It takes BananaChocolatePerBananaSmoothie units of banana chocolate and WaterPerBananaSmoothie units of water to make one banana chocolate smoothie. The number of banana chocolate smoothies made must be more than the number of acai berry smoothies made. Additionally, at least MinAcaiFraction of the total smoothies made must be acai berry smoothies. The smoothie shop has TotalAcaiBerries units of acai berries and TotalBananaChocolate units of banana chocolate. The objective is to determine the number of each type of smoothie to make in order to minimize the total amount of water used."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: e6bf3535-7a86-450d-99e9-4d027ec80bbe
encoding: FLOAT32
metadata:
{"key": "257", "chroma:document": "A handmade sports equipment manufacturing company makes two types of sports equipment: basketballs and footballs. Basketballs require BasketballMaterial units of materials and BasketballHours hours to make, whereas footballs require FootballMaterial units of materials and FootballHours hours to make. The manufacturing company has TotalMaterial units of materials available and their workers can work for at most TotalHours hours. Since basketballs sell better, there must be at least BasketballToFootballRatio times as many basketballs as footballs, but the manufacturing company would like at least MinFootballs footballs. How many of each type of sports equipment should the manufacturing company make to maximize the total number of sports equipment produced?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 86e3e3b1-e11a-43b3-b809-7cb6d711242c
encoding: FLOAT32
metadata:
{"key": "258", "chroma:document": "A researcher must perform two types of experiments, in-vivo and ex-vivo. In-vivo experiments require PrepTimeInVivo minutes to prepare and ExecTimeInVivo minutes to execute. Ex-vivo experiments require PrepTimeExVivo minutes to prepare and ExecTimeExVivo minutes to execute. In-vivo experiments give the researcher RadiationInVivo units of radiation while ex-vivo experiments give the researcher RadiationExVivo units of radiation. At most MaxPrepTime minutes can be used for preparation and MaxExecTime minutes for execution of the experiments. How many of each experiment should be scheduled by the researcher to minimize the total radiation received by the researcher?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: c211f056-93ba-4abe-8065-151d11960679
encoding: FLOAT32
metadata:
{"key": "259", "chroma:document": "A village delivers mail to nearby villages either by runners or canoers. Runners can carry RunnerCapacity bags of mail each time and take RunnerTime hours. Canoers can carry CanoerCapacity bags of mail each time and take CanoerTime hours. At most CanoeProportion of deliveries can be by canoe. Additionally, the village can spare at most TotalHours total hours and at least MinRunners individual runners must be used. How many of each way to deliver must be used to maximize the total amount of mail that can be delivered?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 97343396-5869-491b-ac88-a7d038de5aa2
encoding: FLOAT32
metadata:
{"key": "260", "chroma:document": "A woman on a diet needs to consume two types of meal preps. Each meal prep either provides ProteinPerSmoothie units of protein and CaloriesPerSmoothie calories, or ProteinPerBar units of protein and CaloriesPerBar calories. The woman must consume a number of protein bars equal to RatioBarsToSmoothies times the number of smoothies. She can consume at most MaxCalories calories and aims to maximize her protein intake by choosing the appropriate quantities of meal preps."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 256b33a4-61d0-4c73-8514-91ea6aef2079
encoding: FLOAT32
metadata:
{"key": "261", "chroma:document": "A firm operates NumFactories factories, each producing anti-itch injections and topical cream per hour. Every hour, each factory requires a certain number of plastic units to manufacture the packaging for these products. The total available plastic units are limited, and the firm has to meet minimum production requirements for both anti-itch injections and topical cream. The objective is to determine how many hours to run each factory to minimize the total operational time while satisfying the plastic usage constraint and the production requirements for both products."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 531ff4df-97a6-4bb0-a19a-2189cd924022
encoding: FLOAT32
metadata:
{"key": "262", "chroma:document": "A hospital prepares batches of medication patches and anti-biotic creams. Each medication patch requires TimePerMedPatch minutes to prepare and MaterialsPerMedPatch units of materials. Each anti-biotic cream requires TimePerCream minutes to prepare and MaterialsPerCream units of materials. Since anti-biotic creams are used more often, there must be at least MinCreamPatchRatio times as many anti-biotic creams as medication patches. Due to storage reasons, the hospital can make at most MaxTotalBatches batches of medication patches and anti-biotic creams in total. The hospital has available TotalAvailableMinutes minutes of staff to spare and TotalAvailableMaterials units of materials. If each batch of medication patches can treat PeoplePerMedPatch people and each batch of anti-biotic cream can treat PeoplePerCream people, how many batches of each should be made to maximize the number of people that can be treated?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 1f9ff200-7a37-4732-8280-cb2adb322990
encoding: FLOAT32
metadata:
{"key": "263", "chroma:document": "A company in the desert can transport goods to rural cities either by camel caravans or desert trucks. A camel caravan can deliver GoodsCamelCaravan units of goods per trip and takes HoursCamelCaravan hours. A desert truck can deliver GoodsDesertTruck units per trip and takes HoursDesertTruck hours. The company prefers to have more camel caravans than desert trucks. If the company needs to deliver TotalGoods units of goods, how many of each transportation method should be used to minimize the total number of hours required?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: fd2ec906-4d43-46da-ad0d-6f4bf94d0d4f
encoding: FLOAT32
metadata:
{"key": "265", "chroma:document": "Both chemical A and chemical B need to be added to a mixer for making bread. One unit of chemical A takes TimeA to be effective while one unit of chemical B takes TimeB to be effective. Because chemical A can be dangerous, there has to be at most MaxProportionAtoB as much chemical A as chemical B in the mixer. If there has to be at least MinUnitsA units of chemical A in the mixer and at least MinTotalChemicals units of total chemicals in the mixer, how many units of each should be added to minimize the total time it takes for the mixed bread to be ready?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 20647948-318f-4438-a3d7-0a85bdb0616e
encoding: FLOAT32
metadata:
{"key": "266", "chroma:document": "A senior home has snacks of spinach and soybeans to increase their intake of iron. A cup of spinach contains FibreInSpinach units of fibre and IronInSpinach mg of iron. A cup of soybeans contains FibreInSoybeans units of fibre and IronInSoybeans mg of iron. The number of cups of spinach must exceed the number of cups of soybeans due to other nutritional requirements. Additionally, a cup of spinach contains CaloriesInSpinach calories while a cup of soybeans contains CaloriesInSoybeans calories. The elderly need in total at least TotalFibreRequired units of fibre and TotalIronRequired mg of iron. How many cups of each should the nurses schedule to maximize the seniors\u2019 total caloric intake?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 8e4ccc2f-e93a-42d1-b11b-227234c2e429
encoding: FLOAT32
metadata:
{"key": "267", "chroma:document": "A keyboard manufacturer makes mechanical and standard keyboards. Mechanical keyboards are becoming more popular and thus the manufacturer aims to have MechanicalToStandardRatio times as many mechanical keyboards as standard keyboards. A mechanical keyboard costs PlasticPerMechanicalKeyboard units of plastic and SolderPerMechanicalKeyboard units of solder whereas a standard keyboard costs PlasticPerStandardKeyboard units of plastic and SolderPerStandardKeyboard units of solder. There are still customers that prefer a less noisy alternative. Therefore, there must be at least MinStandardKeyboards standard keyboards. If the company has available TotalPlastic units of plastic and TotalSolder units of solder, how many of each type should be manufactured to maximize the total number of keyboards?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 1d4475e0-eeb6-4603-b759-855322d78938
encoding: FLOAT32
metadata:
{"key": "269", "chroma:document": "A dessert shop needs to decide the quantities of two desserts, matcha ice cream and orange sorbet, to minimize the total amount of flavouring used. Each order of matcha ice cream requires FlavouringMatcha units of flavouring and IceCreamMatcha units of ice cream. Each order of orange sorbet requires FlavouringOrange units of flavouring and WaterOrange units of water. The shop has AvailableIceCream units of ice cream and AvailableWater units of water. At least MinMatchaPercentage percent of the total desserts made must be matcha ice cream. Additionally, the number of orders of orange sorbet must exceed the number of orders of matcha ice cream."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 8cb89e15-162c-4dc7-813e-bdfeb964280b
encoding: FLOAT32
metadata:
{"key": "279", "chroma:document": " Consider a set P described by linear inequality constraints, that is:\n P = {x \\in R^N | a_i^T x <= b_i , i = 1, ..., m}.\n\nwhere a_i \\in R^N and b_i \\in R\n A ball with center y in R^N and radius r is defined as the set of all points within (Euclidean) distance r from y.\nWe are interested in finding a ball with the largest possible radius, which is entirely contained within the set P (The center of such a ball is called the Chebychev center of P."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 07964c02-b05c-4316-a7b4-6093626c0625
encoding: FLOAT32
metadata:
{"key": "297", "chroma:document": " A quantity y is known to depend on another quantity x. A set of corresponding values has been collected for x and y and is presented. The k-th y value takes y_{k} and the k-th x value takes x_{k}.\nFit the \u2018best\u2019 straight line y = bx + a where the objective is to minimize the maximum deviation of all the observed values of y from the value predicted by the linear relationship."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 06aaab03-7a0c-49be-8cab-700a87023cf6
encoding: FLOAT32
metadata:
{"key": "298", "chroma:document": "A quantity y is known to depend on another quantity x. A set of corresponding values has been collected for x and y and is presented. The k-th y value takes y_{k} and the k-th x value takes x_{k}.\nFit the \u2018best\u2019 quadratic curve y = c * x^2 + b * x + a to this set of data points. The objective is to minimize the sum of absolute deviations of each observed value of y from the value predicted by the quadratic relationship."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 32637b5d-fce9-470a-b89b-7a8b2a921188
encoding: FLOAT32
metadata:
{"key": "299", "chroma:document": " A number of power stations are committed to meeting the following electricity load demands over a day. Period t of a day has demand demand_{t}. There are several types of generating unit available: the number of k-th type units is num_{k}. Type k generator has to work between a minimum level minlevel_{k} and a maximum level maxlevel_{k}.  There is an hourly cost of running each type k generator at minimum level runcost_{k}.  In addition, there is an extra hourly cost extracost_{k} for each megawatt at which a type k unit is operated above the minimum level.  Starting up a type k generator also involves a cost startcost_{k}.\nWhich generators should be working in which periods of the day to minimize total cost?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 8195ba4f-2380-48b4-8bb7-f715dc3b4901
encoding: FLOAT32
metadata:
{"key": "300", "chroma:document": " We suppose that some products can be produced, each of them passing through several stages. Necessary time to produce 1 unit of product k is produce_time_{k, s} hours for stage s. Availability in working hours is time_{s} for stage s.  The unitary profits for product k is profit_{k}.\nDetermine the quantities to be produced such that all the production constraints are satisfied and the profit is maximized."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 00155dee-5740-45f4-aaa0-616b501f0a0e
encoding: FLOAT32
metadata:
{"key": "301", "chroma:document": " The knapsack problem has a significant place in the study of integer programming models with binary variables.  In the knapsack problem, one needs to pack a set of items in a container. Each item k has value value_{k} and size size_{k}. And the container has maximum capacity C.  If the total size of the items exceeds the capacity, we can't pack them all.  In that case, the problem is to choose a subset of the items of maximum total value that will fit in the container.\nMaximize the total value of the packed items"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 20ab0a9b-3e51-4383-842f-12346f21a8b9
encoding: FLOAT32
metadata:
{"key": "302", "chroma:document": " We assume that there are available at the market different foods and that the food k sells at a price price_{k} per unit.  In addition there are several basic nutritional ingredients and, to achieve a balanced diet, each individual must receive at least demand_{m} units of nutrient m per day.  Finally, we assume that each unit of food k contains nutri_{k, m} units of nutrition m\nWe want to minimize the total prices of the foods to purchase."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 4bd76bc3-03b3-4f13-9b18-07db938c762d
encoding: FLOAT32
metadata:
{"key": "303", "chroma:document": " Consider the problem of operating a warehouse, by buying and selling the stock of a certain commodity, in order to maximize profit over a certain length of time, say several periods. The warehouse has a fixed capacity, and there is a cost holding_cost per unit for holding stock for one period. The selling price, price_{n}$, of the commodity is known to fluctuate over a number of time periods.  In any period n the price holding for purchase is cost_{n}. The warehouse is originally empty and is required to be empty at the end of the last period.\nDetermine the amount of buying and selling in each period to maximize the profit over the months"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: aaa72fd3-fa6f-4ee4-b6dc-df62ab558f21
encoding: FLOAT32
metadata:
{"key": "304", "chroma:document": " A manufacturer wishes to produce alloy_quant lb of an alloy that consists of several kinds of metals. And by weight, the alloy we want contains a target quantitytarget_{m} of metal metal_{m}. Several other kinds of alloys are available at various prices.  These alloys can be melted to get the alloy we want. Alloy k has ratio_{k, m} ratio of metal_{m} and is sold at price of price_k. Ratio ratio_{k, m} ranges between 0 and 1.0 and should be properly treated in optimization\nThe manufacturer wishes to find the amounts of the various alloys needed and to determine the cheapest combination."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: dac30e84-de32-4eea-81d1-4d17bb33db58
encoding: FLOAT32
metadata:
{"key": "305", "chroma:document": " A small firm specializes in making some types of spare automobile parts.  Each part is has to go through several shops  The required worker-hours for part k in shop s is time_{k, s}. The profit of part k is profit_{k}. The capacity of shop s is capacity_{s} working hours.\nFormulate the problem of determining the quantities of each spare part to be made during the month so as to maximize profit."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: d1d64fbb-ea85-4e3e-bd98-db9b958fb640
encoding: FLOAT32
metadata:
{"key": "306", "chroma:document": " A small computer manufacturing company forecasts the demand over the next n-th month to be demand_{n}. These demands must be satisfied and can not be shorted. In any month it can produce at most max_regular_amount units, using regular production, at a cost of cost_regular dollars per unit.  By using overtime, it can produce additional units at cost_overtime dollars per unit.  The firm can store units from month to month at a cost of store_cost dollars per unit per month.\nFormulate the problem of determining the production schedule that minimizes the cost."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 41f6cd7b-30cc-4370-bd38-495a788e53a1
encoding: FLOAT32
metadata:
{"key": "307", "chroma:document": " To operate a cafeteria, the manager must ensure on-call duty based on the statistics on the required staff.  In the future days, the number of desired employees on day n is denoted with num_{n}. Each employee works n_working_days days in a row and then has n_resting_days days off.\nCalculate the minimum number of employees to hire"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 0c87bf2c-9114-4368-96ce-6f6f50c893d6
encoding: FLOAT32
metadata:
{"key": "310", "chroma:document": " An Italian transport company must send empty containers from its depots to ports.  The number of containers available in the depot i is denoted with numdepot_i.  Container requirement in port j is numport_{j}.  Transport of containers is by barges.  Each barge can only contain two containers and the cost of transport (per barge) is proportional to the distance traveled (price is price Euros/km). The distances between depot i and port j is distance_{i, j}.\nMinimize the total transportation cost."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 9354b82a-7322-4f14-8953-e861699f44b1
encoding: FLOAT32
metadata:
{"key": "312", "chroma:document": " A division of an auto parts manufacturer produces P different parts using M different machines. Batch of 100 part p requires time_{m,p} hours on machine m. The division incurs a charge of cost_{m} per hour for using machine m. Machine m has an availability of up to available_{m} hours per month. The division sells part p in batches of 100 at price of price_{p} per batch. The division must produce at least min_batches_{p} batches of part p each month to fulfill a contract.\nHow many batches of each part should the manufacturer produce each month to maximize profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: fff06a15-0f8f-43fd-b9f8-b010f5ce07b1
encoding: FLOAT32
metadata:
{"key": "313", "chroma:document": " Custom Tees is planning an online advertising campaign with A different ad types across two web companies. The company has set a goal of goal_young thousand clicks from visitors aged 18-25 and goal_old thousand clicks from visitors older than 25. The company has set a goal of goal_unique_young thousand unique clicks from visitors aged 18-25 and goal_unique_old thousand unique clicks from visitors older than 25. Ad type a has an estimated percentage of young_click_{a} clicks from the 18-25 age range. Ad type a has an estimated percentage of old_click_{a} clicks from older visitors. Ad type a has a cost of cost_{a} per 1000 clicks. Ad type a has a maximum allowable clicks of max_click_{a} in thousands. The estimated percentage of unique visitors for each ad type a is unique_click_{a}.\nHow many clicks from each ad type should Custom Tees purchase to minimize cost?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 9b87f534-6add-40a1-8016-a46361b0c4a3
encoding: FLOAT32
metadata:
{"key": "316", "chroma:document": " A fine foods company produces gift baskets for a season that lasts W weeks. The demand for week w is demand_{w} and the demand must be met. Regular labor is available for regular_labor_{w} hours per week and costs $regular_cost/h. Overtime labor is available for overtime_labor_{w} hours per week and costs $overtime_cost/h. Each basket takes assembly_time hours of labor to assemble. The material cost for each basket is $material_cost and it sells for $selling_price. Unsold baskets from a week incur a $holding_cost holding cost.  No baskets are available at the start of week 1. Unsold baskets at the end of week W have a salvage value of $var{salvage_value} and do not incur a holding cost.\nHow much regular and overtime labor should be utilized each week to assemble the baskets to maximize the profit over the season?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: 2caeba22-0a82-43fd-8507-7c48e3e1b18b
encoding: FLOAT32
metadata:
{"key": "317", "chroma:document": " A division of an auto parts manufacturer produces P different parts using M different machines. Batch of 100 part p requires time_{m,p} hours on machine m. The division incurs a charge of cost_{m} per hour for using machine m. Machine m has an availability of up to available_{m} hours per month. Machine M and Machine M-1 can share availability. Individual availability conditions for Machine M and Machine M-1 can be disregarded. The division sells part p in batches of 100 at price of price_{p} per batch. The division must produce at least min_batches_{p} batches of part p each month to fulfill a contract.\nHow many batches of each part should the manufacturer produce each month to maximize profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: bbdd2317-55bc-4ee3-8291-26a838b1c9ac
encoding: FLOAT32
metadata:
{"key": "318", "chroma:document": " A division of an auto parts manufacturer produces P different parts using M different machines. Batch of 100 part p requires time_{m,p} hours on machine m. The division incurs a charge of cost_{m} per hour for using machine m. Machine m has an availability of up to available_{m} hours per month. The division sells part p in batches of 100 at price of price_{p} per batch. The division must produce at least min_batches_{p} batches of part p each month to fulfill a contract. Extra available time for machine m can be acquired at $extra_costs_{m}/hour.  Up to max_extra_{m} hours can be purchased for each machine m.\nHow many batches of each part should the manufacturer produce each month to maximize profit?"}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: c99f9a0a-3f93-4355-9dca-6d57d70825ca
encoding: FLOAT32
metadata:
{"key": "327", "chroma:document": " A team of translators is being assem- bled for the summer Olympics to translate from English into the \\{M} other languages. There is a pool of N translators available. Each translator i can translate into a certain set of languages and comes with a specific cost_i.\nSelect the combination of translators that ensures all required languages can be translated into, at the minimum possible cost."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: e3c1adad-07b6-4fba-8e75-ccb2e9480f1f
encoding: FLOAT32
metadata:
{"key": "328", "chroma:document": "A company has I projects to be done by consultants. They have a choice of J consultants. Each consultant may be assigned up to K projects.  Hiring consultant j incurs a fixed cost of f_j. Assigning project i to consultant j incurs an additional cost of c_{i,j}.\nDetermine the assignment of consultants to projects that minimizes the total cost."}


created_at: 2024-06-11 21:55:15
topic: persistent://default/default/2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
id: b249e0f9-4d8d-4060-88a8-422dc03b9b3e
encoding: FLOAT32
metadata:
{"key": "329", "chroma:document": "The network faces an intrusion that requires immediate intervention. Interventions include isolating nodes or scanning nodes affected by the intruder. Each cluster of nodes must be treated with one intervention type consistently. Interventions can be processed either centrally or through distributed nodes. The processing times for each type of intervention are different across N clusters. The opportunity cost for processing is $central_cost/h for central and $distributed_cost/h for distributed processing. There is a maximum allotment of max_central hours for central processing and max_distributed hours for distributed processing to address the intrusion.\nDetermine the most cost-effective combination of interventions to halt the intruder's progress within the network."}


# collections

id: 2b10f6d3-84c8-4e9c-bb81-9552a7093d4f
name: langchain
database_id: 00000000-0000-0000-0000-000000000000
config_json_str:
{"hnsw_configuration": {"space": "l2", "ef_construction": 100, "ef_search": 10, "num_threads": 32, "M": 16, "resize_factor": 1.2, "batch_size": 100, "sync_threshold": 1000, "_type": "HNSWConfigurationInternal"}, "_type": "CollectionConfigurationInternal"}


# embedding_metadata

key: chroma:document
string_value:
Mrs. Watson wants to invest in the real-estate market and has a total budget of at most TotalBudget. She has two choices which include condos and detached houses. Each dollar invested in condos yields a ProfitPerDollarCondos profit and each dollar invested in detached houses yields a ProfitPerDollarHouses profit. A minimum of MinPercentageCondos of the total investment must be in condos, and at least MinInvestmentDetached must be invested in detached houses.


key: chroma:document
string_value:
A breakfast joint makes two different sandwiches: a regular and a special. Both need eggs and bacon. Each regular sandwich requires EggsPerRegular eggs and BaconPerRegular slices of bacon. Each special sandwich requires EggsPerSpecial eggs and BaconPerSpecial slices of bacon. The joint has a total of TotalEggs eggs and TotalBacon slices of bacon. It makes a profit of ProfitRegular per regular sandwich and a profit of ProfitSpecial per special sandwich. How many of each sandwich should be made to maximize profit?


key: chroma:document
string_value:
A cleaning company aims to maximize exposure for promoting their new product without exceeding their TotalBudget. They will advertise using radio ads and social media ads. Each radio ad costs CostRadioAd and provides ExposureRadioAd exposure. Each social media ad costs CostSocialMediaAd and delivers ExposureSocialMediaAd exposure. The company aims to run between MinRadioAds and MaxRadioAds radio ads and at least MinSocialMediaAds social media ads while staying within the TotalBudget.


key: chroma:document
string_value:
There is TotalGold available that is needed to make long and short cables. Long cables require GoldPerLongCable while short cables require GoldPerShortCable. Because of their compact size, the number of short cables should be at least ShortCableMultiplier times the number of long cables. In addition, there needs to be at least MinLongCables made. If each long cable sold results in a ProfitPerLongCable and each short cable sold results in a ProfitPerShortCable, how many of each type of cable should be made to maximize profit?


key: chroma:document
string_value:
A company is deciding where to promote their product across NumMedia types of media. Each medium has a cost and a number of viewers it attracts per advertisement, defined by CostMedia and ViewersMedia respectively. SzoorchleEngine has a maximum number of advertisements constraint, MaxSzoorchleAds. To balance advertising, at most MaxWassaProportion of the total number of ads should be on Wassa, and at least MinZTubeProportion of the total number of ads should be on ZTube. The total weekly advertising budget is defined by Budget. The goal is to determine the number of advertisements on each type of media to maximize the total audience while adhering to these constraints.


key: chroma:document
string_value:
A furniture company produces two types of products, chairs and dressers. The profit from each chair is ChairProfit, while the profit from each dresser is DresserProfit. Every week, the company has TotalStain gallons of stain and TotalOakWood lengths of oak wood available. Each chair requires StainPerChair gallons of stain and WoodPerChair lengths of oak wood, while each dresser requires StainPerDresser gallons of stain and WoodPerDresser lengths of oak wood. The goal is to determine the number of chairs and dressers to produce in order to maximize the total profit, given the constraints on the availability of stain and oak wood.


key: chroma:document
string_value:
A farmer wants to mix his animal feeds, Feed A and Feed B, in such a way that the mixture will contain a minimum of MinProtein units of protein and MinFat units of fat. Feed A costs CostFeedA per kilogram and contains ProteinFeedA units of protein and FatFeedA units of fat. Feed B costs CostFeedB per kilogram and contains ProteinFeedB units of protein and FatFeedB units of fat. Determine the minimum cost of the mixture.


key: chroma:document
string_value:
An artisan makes two types of terracotta jars: a thin jar and a stubby jar. Each thin jar requires ShapingTimeThinJar minutes of shaping time and BakingTimeThinJar minutes of baking time. Each stubby jar requires ShapingTimeStubbyJar minutes of shaping time and BakingTimeStubbyJar minutes of baking time. Per week, there are TotalShapingTime minutes available for shaping and TotalBakingTime minutes available for baking. The profit per thin jar is ProfitThinJar and the profit per stubby jar is ProfitStubbyJar. How many jars of each type should the artisan make to maximize profit?


key: chroma:document
string_value:
A grocery store wants to liquidate its stock of TotalApples apples, TotalBananas bananas, and TotalGrapes grapes. Given past experience, the store knows that they can propose a banana-haters package with ApplesInBananaHaters apples and GrapesInBananaHaters grapes, and that this package will bring a profit of ProfitBananaHaters euros. Similarly, they can prepare a combo package with ApplesInCombo apples, BananasInCombo bananas, and GrapesInCombo grapes, yielding a profit of ProfitCombo euros. They know they can sell any quantity of these two packages within the availability of its stock. What quantity of each package, banana-haters packages and combo packages, should the store prepare to maximize net profit?


key: chroma:document
string_value:
A bakery uses a stand-mixer and a slow bake oven to make products. Each machine can run for at most MaxHours per year. To produce one unit of bread takes BreadMixerTime time in the stand mixer and BreadOvenTime time in the oven. A unit of cookies requires CookieMixerTime time in the mixer and CookieOvenTime time in the oven. The profit per unit of bread is ProfitBread and the profit per unit of cookies is ProfitCookie. How should the bakery operate to maximize total profit?


key: chroma:document
string_value:
A factory makes two types of glass panes: a regular glass pane and a tempered glass pane. Both require time on a heating and cooling machine. Both machines are available for a maximum of MaxHeatingTime minutes per day for the heating machine and MaxCoolingTime minutes per day for the cooling machine. It takes HeatingTimeRegular minutes in the heating machine and CoolingTimeRegular minutes in the cooling machine to make one regular glass pane. It takes HeatingTimeTempered minutes in the heating machine and CoolingTimeTempered minutes in the cooling machine to make one tempered glass pane. The profit per pane of regular glass is ProfitRegular and the profit per pane of tempered glass is ProfitTempered. How many panes of each glass type should the factory make to maximize profit? What is the maximum profit?


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A shop makes two types of souvenirs, Elephants and Tigers. Each Elephant requires WoodPerElephant amount of wood and PlasticPerElephant amount of plastic. Each Tiger requires WoodPerTiger amount of wood and PlasticPerTiger amount of plastic. The shop has TotalWoodAvailable amount of wood and TotalPlasticAvailable amount of plastic available each week. The profit from selling one Elephant is ProfitPerElephant, and the profit from selling one Tiger is ProfitPerTiger. Determine the number of Elephants and Tigers to make to maximize the total profit.


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The family has TotalInvest amount of money to invest, with some in apartments and the rest in townhouses. The amount of money invested in apartments must not exceed MaxInvestApt. The investment in apartments must be at least a MinRatioInvestAptToTown times the investment in townhouses. The return rate for investment in apartments is ReturnRateApt, and the return rate for investment in townhouses is ReturnRateTown. The goal is to determine the optimal investment in apartments and townhouses to maximize profit.


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An individual needs to take at least MinZ1 grams of Z1 and MinD3 grams of D3 daily. These medicines are available in two types of pills: Zodiac and Sunny. One pill of Zodiac contains Z1InZodiac grams of Z1 and D3InZodiac grams of D3. One pill of Sunny contains Z1InSunny grams of Z1 and D3InSunny grams of D3. The cost per pill of Zodiac is CostZodiac, and the cost per pill of Sunny is CostSunny. The objective is to determine the quantity of Zodiac and Sunny pills that should be taken to meet the medicine requirements at the lowest cost.


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A hobbyist makes model trains and planes using TotalWood and TotalPaint. A model train requires WoodPerTrain units of wood and PaintPerTrain units of paint. A model plane requires WoodPerPlane units of wood and PaintPerPlane units of paint. The hobbyist has available TotalWood units of wood and TotalPaint units of paint. If the profit per model train is ProfitPerTrain and the profit per model plane is ProfitPerPlane, how many of each should be made to maximize his profit?


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A store wants to maximize its profit by optimizing the inventory of phones and laptops. The profit earned per phone is ProfitPhone, and the profit earned per laptop is ProfitLaptop. Each phone requires SpacePhone floor space, and each laptop requires SpaceLaptop floor space, with a total available floor space given by TotalSpace. Corporate policy mandates that at least MinLaptopPercentage of all items in the inventory be laptops. The cost for the store to purchase each phone is CostPhone, and each laptop costs CostLaptop. The store aims to keep the total spending within MaxSpending.


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A candy store mixes different types of candy to prepare two types of products: regular mix and sour surprise mix. Each kilogram of the regular mix contains RegularCandyInRegularMix kilograms of regular candy and SourCandyInRegularMix kilograms of sour candy. The profit per kilogram of the regular mix is ProfitRegularMix. Each kilogram of the sour surprise mix contains RegularCandyInSourMix kilograms of regular candy and SourCandyInSourMix kilograms of sour candy. The profit per kilogram of the sour surprise mix is ProfitSourMix. The candy store has AvailableRegularCandy kilograms of regular candy and AvailableSourCandy kilograms of sour candy available. The goal is to determine how many kilograms of each type of product should be created to maximize the total profit given the available candy.


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A factory has TotalSpace of space to allocate between the production of phones and laptops, where each type of product occupies a certain amount of space per unit of production. Phones require PhoneLabor hours of labor and cost PhoneCost per square foot of space allocated for phone production. Laptops require LaptopLabor hours of labor and cost LaptopCost per square foot of space allocated for laptop production. Phones produce a net revenue of PhoneRevenue per square foot while laptops produce a net revenue of LaptopRevenue per square foot. The factory aims to spend at most TotalBudget and use at most TotalLabor hours of labor. The goal is to determine the optimal allocation of TotalSpace between phones and laptops to maximize total net revenue.


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An electronics store sells premium desktops with more power as well as regular desktops for everyday use. Each premium desktop costs the store CostPremium to make and yields a profit of ProfitPremium. Each regular desktop costs the store CostRegular to make and yields a profit of ProfitRegular. The store sells at most MaxDesktops desktops each month and wants to spend at most MaxBudget on making the desktops. How many of each should be made and sold to maximize profit?


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A car manufacturer makes two versions of the same car, a regular model and a premium model. They make x1 regular models per day and x2 premium models per day. The profit per regular model is ProfitRegular and the profit per premium model is ProfitPremium (x1 and x2 are unknown values both greater than or equal to 0). The daily demand for these cars is limited to at most MaxDemandRegular regular models and MaxDemandPremium premium models. In addition, the manufacturer can make a maximum of MaxTotalProduction cars of either type per day. How many cars of each model should the manufacturer make in order to maximize profit?


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You are designing an office space with two types of desks: long desks and short desks. You can spend at most Budget. Long desks cost CostLongDesk, take up SpaceLongDesk of space, and seat SeatingLongDesk employees. Short desks cost CostShortDesk, take up SpaceShortDesk of space, and seat SeatingShortDesk employees. The office can have at most MaxSpace of desks. How many of each desk should you buy in order to maximize the seating availability?


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Ayse produces a plant growth compound by mixing two types of fertilizer: C and Y. This growth compound must contain at least MinRequiredNitrousOxide units of nitrous oxide and MinRequiredVitaminMix units of vitamin mix. Fertilizer C and Y cost CostPerKgFertilizerC and CostPerKgFertilizerY per kg respectively. Fertilizer C contains NitrousOxidePerKgC units of nitrous oxide per kg and VitaminMixPerKgC units of vitamin mix per kg. Fertilizer Y contains NitrousOxidePerKgY units of nitrous oxide per kg and VitaminMixPerKgY units of vitamin mix per kg. Determine the minimum cost of Ayse's compound.


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A car manufacturer makes NumOilTypes types of car oils. A container of each oil type contains different amounts of NumSubstances substances. The car manufacturer has a certain total amount of each substance available. Additionally, the profit per container of each oil type is given. The manufacturer wants to determine how many containers of each oil type should be made to maximize profit.


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A food truck owner can spend at most TotalBudget on purchasing mangos and guavas. A mango costs MangoCost and a guava costs GuavaCost. Each mango is sold for a profit of MangoProfit while each guava is sold for a profit of GuavaProfit. The owner estimates that at least MinMangosSold but at most MaxMangosSold mangos are sold each month. He also estimates that the number of guavas sold is at most MaxGuavasPerMango of the mangos sold. The objective is to determine how many mangos and guavas should be sold to maximize the profit.


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A nutritionist is making a special vitamin mix using two drinks: A and B. The vitamin mix must contain at least MinVitaminA units of Vitamin A, at least MinVitaminD units of Vitamin D, and at most MaxVitaminE units of Vitamin E. A cup of drink A contains VitaminAInA units of Vitamin A, VitaminDInA units of Vitamin D, VitaminEInA units of Vitamin E, and VitaminKInA units of Vitamin K. A cup of drink B contains VitaminAInB units of Vitamin A, VitaminDInB units of Vitamin D, VitaminEInB units of Vitamin E, and VitaminKInB units of Vitamin K. How many cups of each drink should be used to make the vitamin mix in order to minimize the amount of Vitamin K?


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An ice cream store makes two types of ice cream, chocolate and vanilla. In a week, they must produce at least MinChocolateGallons and at most MaxChocolateGallons of chocolate ice cream, and at least MinVanillaGallons and at most MaxVanillaGallons of vanilla ice cream. The time required to produce one gallon of chocolate ice cream is TimePerGallonChocolate hours, and the time required to produce one gallon of vanilla ice cream is TimePerGallonVanilla hours. The total available time for production in a week is TotalAvailableHours hours. Additionally, at least MinWorkers workers are needed at any time, with at least WorkersPerGallonChocolate workers working on chocolate ice cream and at least WorkersPerGallonVanilla workers working on vanilla ice cream. The profit per gallon of chocolate ice cream is ProfitPerGallonChocolate, and the profit per gallon of vanilla ice cream is ProfitPerGallonVanilla. The objective is to determine the number of gallons of each type of ice cream to produce in order to maximize profit.


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Mark has TotalLand acres of land available to grow potatoes and cucumbers that he sells at a farmers' market. He must grow at least MinPotatoes acres of potatoes and MinCucumbers acres of cucumbers to meet his contract. Mark prefers to grow more cucumbers than potatoes, but he only has enough resources to grow at most MaxCucumberToPotatoRatio times the amount of cucumbers as potatoes. If the profit per acre of potatoes is ProfitPerAcrePotato and the profit per acre of cucumbers is ProfitPerAcreCucumber, how many acres of each should he grow to maximize his profit? What is that profit?


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A flooring company produces hardwood and vinyl planks. The demand for hardwood flooring each week is at least MinDemandHardwood square feet, and the demand for vinyl planks each week is at least MinDemandVinyl square feet. The total amount of flooring shipped each week must be at least MinTotalShipment square feet. Due to a labor shortage, the company can produce no more than MaxProductionHardwood square feet of hardwood flooring and no more than MaxProductionVinyl square feet of vinyl planks each week. The profit from producing a square foot of hardwood flooring is ProfitHardwood, while the profit from producing a square foot of vinyl planks is ProfitVinyl. The goal is to determine the number of square feet of each type of flooring to produce each week to maximize the company’s profit.


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A farmer has two farms, where he grows NumBerryTypes different types of berries. He has a contract to provide specific quantities of each type of berry to a local store (DeliveryRequirement). It costs OldFarmCost to operate the old farm per day, where OldFarmOutput of each type of berry can be harvested and delivered in a day. It costs NewFarmCost to operate the new farm per day, where NewFarmOutput of each type of berry is harvested and delivered in a day. The goal is to meet the DeliveryRequirement for each type of berry while minimizing the total operation cost.


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Jordan wants to design a diet consisting of items Rice and Kebab. The cost per serving of Rice is represented by CostRice, and the cost per serving of Kebab is represented by CostKebab. Each serving of Rice provides CaloriesRice calories and ProteinRice grams of protein, while each serving of Kebab provides CaloriesKebab calories and ProteinKebab grams of protein. The goal is to minimize the total cost of the diet while ensuring that the total daily calorie intake is at least MinCalories calories and the total daily protein intake is at least MinProtein grams.


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A company sells custom scooters and bikes. The ProfitPerScooter and ProfitPerBike are given as abstract symbols. Each scooter requires DesignTimePerScooter with the design team and EngineeringTimePerScooter with the engineering team. Each bike requires DesignTimePerBike with the design team and EngineeringTimePerBike with the engineering team. Per month, there are TotalDesignHours available on the design team and TotalEngineeringHours available on the engineering team. Determine the monthly production quantities of scooters and bikes to maximize profit.


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A person only eats two types of food: vegetables and fruits. Each serving of vegetables contains a certain amount of vitamins and minerals, and each serving of fruits contains a different amount of vitamins and minerals. The person wants to consume a minimum required amount of vitamins and minerals. The cost per serving of vegetables and fruits is specified. The goal is to determine the number of servings of vegetables and fruits to consume in order to meet the minimum vitamin and mineral requirements while minimizing the total cost.


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A bakery bakes two types of products: bagels and croissants. A batch of bagels requires OvenTimeBagels of oven time and ChefTimeBagels of pastry chef time. A batch of croissants requires OvenTimeCroissants of oven time and ChefTimeCroissants of pastry chef time. The bakery has a maximum of MaxOvenTime hours available for the oven and MaxChefTime hours available for the pastry chef each day. The profit per batch is ProfitBagels for bagels and ProfitCroissants for croissants. The objective is to maximize profit using the available capacity.


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A teddy bear company produces three different colored bears using two factories. Running the first factory for one hour costs CostFactory1 and produces ProductionBlackFactory1 black teddy bears, ProductionWhiteFactory1 white teddy bears, and ProductionBrownFactory1 brown teddy bears. Running the second factory for one hour costs CostFactory2 and produces ProductionBlackFactory2 black teddy bears and ProductionWhiteFactory2 white teddy bears but no brown teddy bears. The company needs to meet a daily demand of at least DemandBlack black teddy bears, DemandWhite white teddy bears, and DemandBrown brown teddy bears. The goal is to minimize the cost of production while fulfilling the demand.


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A farmer has TotalAcres acres of land to grow turnips and pumpkins. Turnips require WateringPerAcreTurnips minutes of watering and PesticidePerAcreTurnips worth of pesticide per acre. Pumpkins require WateringPerAcrePumpkins minutes of watering and PesticidePerAcrePumpkins worth of pesticide per acre. The farmer has TotalWateringTime minutes available for watering and TotalPesticideBudget available to spend on pesticide. If the revenue per acre of turnips is RevenuePerAcreTurnips and the revenue per acre of pumpkins is RevenuePerAcrePumpkins, how many acres of each should he grow to maximize his revenue.


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A school employs staff and substitute teachers. Per shift, staff teachers work StaffHoursPerShift hours and get paid StaffWagePerShift. Per shift, substitute teachers work SubstituteHoursPerShift hours and get paid SubstituteWagePerShift. The school requires RequiredHours of teaching availability. If the school has a budget of TotalBudget, how many of each teacher should be hired to minimize the total number of teachers?


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A factory uses HighIntensityDrills and LowIntensityDrills to process DailyGemProcessingRequirement gems each day. Each HighIntensityDrill has a capacity of HighIntensityDrillCapacity gems and requires HighIntensityDrillWaterRequirement units of water per day. Each LowIntensityDrill has a capacity of LowIntensityDrillCapacity gems and requires LowIntensityDrillWaterRequirement units of water per day. The total available water per day is TotalAvailableWater. At most MaxFractionHighIntensityDrills of the drills can be HighIntensityDrills, and at least MinLowIntensityDrills of the drills must be LowIntensityDrills. The goal is to determine the number of HighIntensityDrills and LowIntensityDrills required to minimize the total number of drills needed.


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A sandwich company can open two types of stores: dine-in places, each requiring EmployeesDineIn employees and producing ProductionDineIn sandwiches per day, and food-trucks, each requiring EmployeesFoodTruck employees and producing ProductionFoodTruck sandwiches per day. The company must produce at least MinProduction sandwiches per day and has TotalEmployees employees available. The objective is to determine how many of each type of store to open to minimize the total number of stores.


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There are two processes, process A and process B, to plate coins with gold. Process A requires GoldRequiredA units of gold, WiresRequiredA number of wires, and can plate CoinsPlatedA number of coins. Process B requires GoldRequiredB units of gold, WiresRequiredB number of wires, and can plate CoinsPlatedB number of coins. There are TotalGoldAvailable units of gold and TotalWiresAvailable number of wires available. How many processes of each type should be run to maximize the total number of coins that can be plated?


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A woodshop can purchase two types of saws, a miter saw and a circular saw. A miter saw has a cutting capacity of MiterCutCapacity and produces MiterSawdust units of sawdust per day. A circular saw has a cutting capacity of CircularCutCapacity and produces CircularSawdust units of sawdust per day. The woodshop must cut at least MinPlanks planks of wood per day. However, to avoid too much pollution, they can produce at most MaxSawdust units of sawdust per day. The goal is to determine how many of each type of saw should be purchased to minimize the total number of saws needed.


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A farmer has TotalAcres of land on which he must process hay using either a windrower or hay harvester. For each acre of land, the windrower can process WindrowerHayPerAcre of hay while the hay harvester can process HarvesterHayPerAcre of hay. Per acre, the windrower produces WindrowerMethanePerAcre of methane gas and requires WindrowerFuelPerAcre of fuel. On the other hand, the hay harvester produces HarvesterMethanePerAcre of methane gas per acre and requires HarvesterFuelPerAcre of fuel. There are TotalFuel of fuel available and the farmer can produce at most MaxMethane of methane gas. For how many acres should each machine be used to maximize the amount of hay processed?


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A fast food place makes two types of food items. Each 'Wrap' requires 'MeatPerWrap' units of meat and 'RicePerWrap' units of rice, and each 'Platter' requires 'MeatPerPlatter' units of meat and 'RicePerPlatter' units of rice. The time required to make one Wrap is 'TimePerWrap' and the time required to make one Platter is 'TimePerPlatter'. The fast food place must use at least 'MinMeat' units of meat and 'MinRice' units of rice. Additionally, the number of Wraps produced must be at least 'WrapsToPlattersRatio' times the number of Platters produced. The objective is to determine the number of each type of food item to make in order to minimize the total production time.


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An amusement park is installing ticket machines, both cash-based and card-only machines. A cash-based machine can process CashMachineCapacity people per hour while a card-only machine can process CardMachineCapacity people per hour. The cash-based machine needs CashPaperConsumption rolls of paper per hour while the card-only machine requires CardPaperConsumption rolls of paper per hour. The amusement park needs to be able to process at least MinTotalPeopleRequirement people per hour but can use at most MaxTotalPaperLimit rolls of paper per hour. Also, the number of card-only machines must not exceed the number of cash-based machines.


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A honey farmer sells his honey in glass and plastic jars. A glass jar can hold HoneyPerGlassJar of honey while a plastic jar can hold HoneyPerPlasticJar of honey. Since glass jars are more expensive, at least MinPlasticPerGlass times as many plastic jars must be filled as glass jars. However, at least MinGlassJars glass jars should be filled. If the farmer has TotalHoney of honey, how many jars of each should be filled to maximize the total number of bottles filled?


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A high rise building is buying two types of furnaces, a new model and an old model. A new model furnace has a HeatingCapacityNew and consumes ElectricityConsumptionNew per day. An old model furnace has a HeatingCapacityOld and consumes ElectricityConsumptionOld per day. At most MaxProportionOld of the furnaces can be the old model and at least MinNumNew new model furnaces should be used. The building needs to heat at least TotalApartments and has TotalElectricity available. Determine the number of new and old model furnaces to purchase in order to minimize the total number of furnaces.


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A company needs to determine the number of rural and urban factories to build in order to minimize the total number of factories. A rural factory produces PhonesPerDayRural phones per day and requires ManagersRural managers. An urban factory produces PhonesPerDayUrban phones per day and requires ManagersUrban managers. The company has TotalManagers managers available and must produce at least MinPhonesPerDay phones per day.


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An ice cream store can buy two types of machines, a counter-top one and a fridge-sized one, to make ice cream. The counter-top machine can produce CounterTopCapacity cones worth of ice cream every day while producing CounterTopHeatOutput units of heat. The fridge-sized machine can produce FridgeCapacity cones worth of ice cream every day while producing FridgeHeatOutput units of heat. The ice cream store can output at most MaxDailyHeatOutput units of heat per day and must produce at least MinDailyProduction cones worth of ice cream. How many of each machine should they buy to minimize the total number of machines needed?


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There are NumContainers specialized containers that are used to make a pharmaceutical paste. Each type of container requires WaterRequired of water and PillRequired of powdered pill to produce PasteProduced of paste. The pharmacy has a TotalWater amount of water and a TotalPill amount of powdered pill available. How many of each type of container should be used to maximize the amount of paste that can be made?


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A company operates on TotalAcres of land where they use oil wells of small and large size. Per acre of land, a small oil well can produce OilProductionSmall units of oil. Per acre of land, a large oil well can produce OilProductionLarge units of oil. However, a small oil well produces PollutionSmall units of pollution and requires DrillBitsSmall drill bits per acre, and a large oil well produces PollutionLarge units of pollution and requires DrillBitsLarge drill bits per acre. The company has TotalDrillBits drill bits available and can produce at most MaxPollution units of pollution due to strict environmental laws. How many acres should be allocated to small and large oil wells to maximize the total oil production?


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A bakery makes two types of croissants. The first type of croissant requires ButterAlmond units of butter and FlourAlmond units of flour. The second type of croissant requires ButterPistachio units of butter and FlourPistachio units of flour. The bakery has a total of TotalButter units of butter and TotalFlour units of flour available. The number of the first type of croissants produced should be at least MinRatioAlmondToPistachio times the number of the second type of croissants. The time required to produce one unit of the first type of croissant is TimeAlmond, and the time required to produce one unit of the second type of croissant is TimePistachio. The objective is to determine the number of each type of croissant to produce in order to minimize the total production time.


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A burger chain is buying both gas and electric grills to make burger patties. A gas grill can cook PattiesPerGasGrill patties per minute while an electric grill can cook PattiesPerElectricGrill patties per minute. The gas grill requires OilPerGasGrill units of cooking oil per minute while the electric grill requires OilPerElectricGrill units of cooking oil per minute. The number of electric grills must be less than the number of gas grills. The burger chain wants to be able to make at least MinPattiesPerMinute patties per minute and use at most MaxOilPerMinute units of cooking oil per minute. How many of each grill should be bought to minimize the total number of grills?


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A company sells cough syrup in kids and adult size bottles. A kids size bottle can hold VolumeKids of cough syrup while an adult size bottle can hold VolumeAdult of cough syrup. Since there is no difference in concentration of medical ingredients between the two bottles, the number of adult size bottles must be at least MinRatioAdultToKids times the number of kids size bottles. However, at least MinKidsBottles kids size bottles must be made. If the company has TotalCoughSyrup of cough syrup available, how many bottles of each should be made to maximize the total number of bottles?


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A bakery makes brownies and lemon squares. Each brownie requires ChocolateMixPerBrownie units of chocolate mix and FiberPerBrownie units of fiber. Each lemon square requires LemonMixPerLemonSquare units of lemon mix and FiberPerLemonSquare units of fiber. Lemon squares sell faster, so the number of lemon squares made must be larger than the number of brownies made. At least MinBrowniesRatio of the items made must be brownies. The bakery has TotalChocolateMix units of chocolate mix and TotalLemonMix units of lemon mix. The goal is to determine the number of each type of item to make in order to minimize the total amount of fiber needed.


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A clinic employs nurses and pharmacists to deliver shots to patients. A nurse works NurseHoursPerShift per shift while a pharmacist works PharmacistHoursPerShift per shift. Nurses are paid NursePaymentPerShift per shift while pharmacists are paid PharmacistPaymentPerShift per shift. The clinic needs TotalLaborHoursRequired of healthcare labor to meet needs. If the firm has a budget of TotalBudget, how many of each healthcare worker should be scheduled to minimize the total number of workers?


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A laundromat can buy two types of washing machines, a top-loading model and a front-loading model. The top-loading model can wash WashingCapacityTopLoading items per day while the front-loading model can wash WashingCapacityFrontLoading items per day. The top-loading model consumes EnergyConsumptionTopLoading kWh per day while the front-loading model consumes EnergyConsumptionFrontLoading kWh per day. The laundromat must be able to wash at least MinWashingCapacityRequired items per day and has available MaxEnergyAvailable kWh per day. Since the top-loading machines are harder to use, at most MaxPercentageTopLoading of the machines can be top-loading. Further, at least MinFrontLoadingMachines should be front-loading. How many of each machine should the laundromat buy to minimize the total number of washing machines?


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A shipping company can purchase RegularVans and HybridVans to make deliveries. A RegularVan can deliver RegularVanCapacity packages per day and produces RegularVanPollution units of pollutants. A HybridVan can deliver HybridVanCapacity packages per day and produces HybridVanPollution units of pollutants. Due to a new environmental law, they can produce at most MaxPollution units of pollutants per day. However, the company needs to be able to deliver at least MinPackages packages per day. How many of each type of van should they buy to minimize the total number of vans needed?


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The objective is to maximize the amount of carbon dioxide produced using two different processes: one with a catalyst and one without a catalyst. The process with a catalyst requires 'WoodWithCatalyst' units of wood and 'OxygenWithCatalyst' units of oxygen to produce 'CO2WithCatalyst' units of carbon dioxide. The process without a catalyst requires 'WoodWithoutCatalyst' units of wood and 'OxygenWithoutCatalyst' units of oxygen to produce 'CO2WithoutCatalyst' units of carbon dioxide. The total available resources are 'TotalWood' units of wood and 'TotalOxygen' units of oxygen. The decision variables are the number of times the process with a catalyst is used and the number of times the process without a catalyst is used. The aim is to find the optimal number of each process to maximize the total production of carbon dioxide, subject to the constraints on the availability of wood and oxygen.


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A tea estate has TotalLand acres of land available and they need to pick the tea leaves either using a traditional machine or modern machine. For each acre of land, the traditional machine can pick TealeavesTraditional kg of tea leaves, creates WasteTraditional kg of waste, and requires FuelTraditional liters of fuel. For each acre of land, the modern machine can pick TealeavesModern kg of tea leaves, creates WasteModern kg of waste, and requires FuelModern liters of fuel. The estate has available TotalFuel liters of fuel and can handle at most MaxWaste kg of waste. For how many acres should each machine be used to maximize the amount of tea leaves that can be picked?


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An organization is purchasing 2 different models of stamping machines. Each model has a specific StampingRate and GlueConsumption per minute. The number of the first model of machines must be less than the number of the second model. Additionally, the organization aims to ensure they can process at least MinLetters letters per minute and use at most MaxGlue units of glue per minute. The objective is to determine the number of each model of stamping machines to minimize the total number of stamping machines.


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A company sells their bananas in small and large crates. A small crate can hold BananasPerSmallCrate bananas while a large crate can hold BananasPerLargeCrate bananas. The number of large crates must be at least MinLargeToSmallRatio times the number of small crates. However, at least MinSmallCrates small crates should be used. If the company has TotalBananas available bananas, how many of each crate should the company use to maximize the total number of crates used?


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A store sells two types of crepes: chocolate crepes and peanut butter crepes. A chocolate crepe requires ChocolateSpreadForChocolateCrepe units of chocolate spread and CrepeMixForChocolateCrepe units of crepe mix. A peanut butter crepe requires PeanutButterSpreadForPeanutButterCrepe units of peanut butter spread and CrepeMixForPeanutButterCrepe units of crepe mix. The number of peanut butter crepes made (NumPeanutButterCrepes) must exceed the number of chocolate crepes made (NumChocolateCrepes). Additionally, at least MinimumChocolateCrepeProportion of the total crepes made should be chocolate crepes, i.e., NumChocolateCrepes should be at least MinimumChocolateCrepeProportion * (NumChocolateCrepes + NumPeanutButterCrepes). The store has TotalChocolateSpread units of chocolate spread and TotalPeanutButterSpread units of peanut butter spread available. The total amount of chocolate spread used by all chocolate crepes must not exceed TotalChocolateSpread, and the total amount of peanut butter spread used by all peanut butter crepes must not exceed TotalPeanutButterSpread. The objective is to determine NumChocolateCrepes and NumPeanutButterCrepes to minimize the total amount of crepe mix needed while satisfying these constraints.


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A fire department employs regular and emergency fire fighters. A regular fire fighter works HoursRegularShift per shift and earns EarningsRegular. An emergency fire fighter works HoursEmergencyShift per shift and earns EarningsEmergency. Due to wildfires in the region, the fire department needs at least MinHoursRequired hours of fire fighter time. If the fire department has a budget of Budget, how many of each should the fire department hire to minimize the total number of fire fighters?


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A mall buys two types of hand sanitizer machines, which have delivery rates defined by 'DeliverRate' and energy consumptions defined by 'EnergyConsumption'. Due to hygiene concerns, at most 'MaxManualPercentage' of the machines can be manual, and at least 'MinMotionActivated' must be motion activated. The mall must achieve a minimum total delivery rate of 'MinDeliverRate' and adhere to a maximum total energy consumption of 'MaxEnergyConsumption'. The goal is to determine the number of each type of machine to minimize the total number of machines.


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A company can build two types of shops: a small shop and a large shop. A small shop can produce HotDogsPerDaySmallShop hot dogs per day and requires WorkersPerSmallShop workers. A large shop can produce HotDogsPerDayLargeShop hot dogs per day and requires WorkersPerLargeShop workers. The company must produce at least MinHotDogsPerDay hot dogs per day but only has TotalWorkers workers available. How many of each type of shop should the company build to minimize the total number of shops?


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An airport buys two types of vehicles, a 4-wheeler and 3-wheeler, to help move luggage. A 4-wheeler vehicle can move LuggageCapacity4Wheeler luggage per day and produces Pollution4Wheeler units of pollutant per day. A 3-wheeler vehicle can move LuggageCapacity3Wheeler luggage per day and produces Pollution3Wheeler units of pollutant per day. The airport needs to be able to move at least MinLuggage luggage per day. To avoid over-polluting the airport, they can produce at most MaxPollution units of pollutant per day. How many of each vehicle should the airport buy to minimize the total number of vehicles needed.


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A man fishes in a TotalArea lake and can catch fish either using a net or fishing line. For each acre of the lake, using a net will catch FishCaughtNet fish and requires BaitRequiredNet units of bait but also causes PainNet units of pain for the fisherman. For each acre of the lake, using a fishing line will catch FishCaughtLine fish and requires BaitRequiredLine units of bait but also causes PainLine units of pain for the fisherman. The fisherman has available TotalBait units of bait and can tolerate at most MaxPain units of pain. For how many acres each should he use each fishing method to maximize the amount of fish he can catch?


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A coffee shop sells two types of coffee: mochas and regular coffees. Each type requires specific units of coffee powder (CoffeePowderPerMocha, CoffeePowderPerRegular) and milk (MilkPerMocha, MilkPerRegular), which are limited in total availability (TotalCoffeePowder, TotalMilk). Producing each type also requires a specific amount of time (TimePerMocha, TimePerRegular). Additionally, there is a constraint specifying that the number of mochas made must be at least a certain multiple (MochaToRegularRatio) of the number of regular coffees made. The goal is to determine the number of each type of coffee to produce in order to minimize the total production time, given these constraints.


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A butcher shop is buying slicers for their shop, a manual slicer and an automatic slicer. The manual slicer has a Cutting Rate (ManualCutRate) and uses grease at a rate (ManualGreaseRate). The automatic slicer has a Cutting Rate (AutomaticCutRate) and uses grease at a rate (AutomaticGreaseRate). The number of manual slicers should be less than the number of automatic slicers. The butcher shop must meet a minimum requirement of slices per minute (MinSlices) and adhere to a maximum grease usage per minute (MaxGrease). The goal is to determine the number of each slicer to minimize the total number of slicers in the shop.


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A water company sells water in glass and plastic bottles. A glass bottle can hold GlassBottleCapacity of water while a plastic bottle can hold PlasticBottleCapacity of water. Because most customers prefer plastic bottles, the number of plastic bottles must be at least MinPlasticToGlassRatio times the number of glass bottles. However, there must be at least MinGlassBottles glass bottles. If the company has available TotalWater of water, how many of each bottle should be made to maximize the total number of bottles?


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A restaurant makes two types of curry: goat curry and chicken curry. Each bowl of goat curry requires GoatMeatPerGoatCurry units of goat meat and CurryBasePerGoatCurry units of curry base. Each bowl of chicken curry requires ChickenMeatPerChickenCurry units of chicken meat and CurryBasePerChickenCurry units of curry base. The restaurant has TotalGoatMeat units of goat meat and TotalChickenMeat units of chicken meat available. At least MinChickenCurryPercentage percentage of the total bowls made must be chicken curry, and the number of goat curry bowls must be larger than the number of chicken curry bowls. The objective is to determine the number of each type of curry bowl to make so as to minimize the total usage of curry base.


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An accounting firm employs part time workers and full time workers. Full time workers work HoursPerShiftFullTime per shift while part time workers work HoursPerShiftPartTime per shift. In addition, full time workers are paid WageFullTime per shift while part time workers are paid WagePartTime per shift. Currently, the accounting firm has a project requiring TotalLaborHours of labor. If the firm has a TotalBudget for wages, determine the number of each type of worker to schedule in order to minimize the total number of workers, subject to the constraints of meeting the required labor hours and the budget.


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A factory has two types of machines. Each machine of the first type can produce ItemsMachineA items and consumes ElectricityMachineA kWh per day. Each machine of the second type can produce ItemsMachineB items and consumes ElectricityMachineB kWh per day. The factory needs to produce at least MinItemsPerDay items per day and has MaxElectricityPerDay kWh of electricity available per day. At most MaxPercentageB of the machines can be of the second type. Additionally, at least MinMachinesA of the machines must be of the first type. The objective is to find the number of each type of machine to use to minimize the total number of machines.


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A chemical plant can buy two types of generators, generator A and generator B, which use two different processes to generate hydrogen. Generator A uses an electrolysis process and produces HydrogenProductionA of hydrogen as well as PollutantProductionA of pollutants every day. Generator B uses a fermentation process to produce HydrogenProductionB of hydrogen per day while outputting PollutantProductionB of pollutants. The chemical plant must make a minimum of MinHydrogenRequirement of hydrogen per day but due to environmental restrictions they can produce at most MaxPollutantAllowance of pollutant. The goal is to determine the quantities, CountA and CountB, of each type of generator to minimize the total number of generators needed.


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There are two chemical reactions, chemical reaction A and chemical reaction B. Chemical reaction A requires InertGasA units of rare inert gas and TreatedWaterA units of treated water to produce CompoundA units of a rare compound. Chemical reaction B requires InertGasB units of rare inert gas and TreatedWaterB units of treated water to produce CompoundB units of a rare compound. There are TotalInertGas units of rare inert gas and TotalTreatedWater units of treated water available in the lab. The objective is to determine the number of reactions of type A (XA) and type B (XB) to maximize the total amount of the rare compound produced.


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A mining company has available TotalLand square miles of mining sites and is considering the use of two mining techniques: heap leaching and vat leaching. For each square mile of land, heap leaching technique can have a daily production of HeapLeachingProduction of rare earth oxide per square mile but it also creates HeapLeachingWastewater of polluted wastewater and requires HeapLeachingMachines of extraction machines. On the other hand, vat leaching technique produces VatLeachingProduction of rare earth oxide per square mile per day while creating VatLeachingWastewater of polluted wastewater and requiring VatLeachingMachines of extraction machines. There are TotalMachines available and due to environmental regulations, the amount of polluted wastewater must be at most MaxWastewater daily. Find the proportion of lands that use each mining technique in order to maximize the daily production of rare earth oxide.


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A small chocolate shop makes two types of chocolate bars: milk and dark. Milk chocolate bars require CocoaPerMilkChocolate units of cocoa and MilkPerMilkChocolate units of milk. Dark chocolate bars require CocoaPerDarkChocolate units of cocoa and MilkPerDarkChocolate units of milk. The shop has TotalCocoa units of cocoa and TotalMilk units of milk available. Additionally, at least MilkToDarkRatio times as many milk chocolate bars need to be produced as dark chocolate bars. To minimize the total production time, where producing one milk chocolate bar takes TimePerMilkChocolate minutes and one dark chocolate bar takes TimePerDarkChocolate minutes, how many of each type of chocolate bar should be produced?


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An office is buying two types of printers: a premium model and a regular model. The premium model can print PagesPerMinutePremium pages per minute and the regular model can print PagesPerMinuteRegular pages per minute. Additionally, the premium model requires InkPerMinutePremium units of ink per minute, while the regular model requires InkPerMinuteRegular units of ink per minute. The office wants to ensure at least MinPagesPerMinute pages can be printed per minute, and at most MaxInkPerMinute units of ink can be used per minute. The number of regular printers must be less than the number of premium printers to minimize the total number of printers in the office.


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A company sells two types of bottles: a vintage bottle with volume VolumeVintage and a regular bottle with volume VolumeRegular. The company has a total available volume of TotalVolume. The number of regular bottles must be at least MinRatioRegularToVintage times the number of vintage bottles. Additionally, there is a requirement to produce at least MinVintageBottles vintage bottles. The goal is to determine how many of each type of bottle should be produced in order to maximize the total number of bottles.


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A patient in the hospital can take two pills, Pill 1 and Pill 2. Per pill, Pill 1 provides PainMedPill1 units of pain medication and AnxietyMedPill1 units of anxiety medication. Per pill, Pill 2 provides PainMedPill2 units of pain medication and AnxietyMedPill2 units of anxiety medication. In addition, Pill 1 causes DischargePill1 units of discharge while Pill 2 causes DischargePill2 units of discharge. At most MaxPainMed units of pain medication can be provided and at least MinAnxietyMed units of anxiety medication must be provided. How many pills of each should the patient be given to minimize the total amount of discharge?


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A man on a strict diet consumes drinks from two brands, alpha and omega. Each alpha brand drink contains ProteinAlpha grams of protein, SugarAlpha grams of sugar, and CaloriesAlpha calories per bottle. Each omega brand drink contains ProteinOmega grams of protein, SugarOmega grams of sugar, and CaloriesOmega calories per bottle. The man wants to consume at least MinProtein grams of protein and MinCalories calories. Additionally, the omega brand drink should constitute at most MaxOmegaProportion of his total drink intake. The goal is to find the number of bottles of each brand he should drink to minimize his sugar intake.


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A summer camp conducts science experiments using NumBeakers different types of beakers. Each beaker i requires FlourRequired[i] units of flour and LiquidRequired[i] units of special liquid to produce SlimeProduced[i] units of slime, and generates WasteProduced[i] units of waste. The summer camp has a total of TotalFlour units of flour and TotalLiquid units of special liquid available. The maximum allowable waste that can be produced is MaxWaste units. The goal is to determine the number of each beaker type to use in order to maximize the total amount of slime produced.


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A dog hospital has TotalToothMedication units of tooth medication to make both small and large bones. A small bone requires ToothMedicationSmall units of tooth medication and MeatSmall units of meat. A large bone requires ToothMedicationLarge units of tooth medication and MeatLarge units of meat. Since most dogs prefer small bones, at least MinPercentageSmallBones percent of the bones made must be small. In addition, the hospital must make at least MinLargeBones large bones. How many of each bone should be made to minimize the amount of meat needed?


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A scientist in the arctic needs to consume enough vitamin D and vitamin C by drinking two types of juice: orange juice and apple juice. Each box of orange juice contains VitDOrangeJuice units of vitamin D and VitCOrangeJuice units of vitamin C. Each box of apple juice contains VitDAppleJuice units of vitamin D and VitCAppleJuice units of vitamin C. Since the scientist prefers apple juice, he must drink at least MinAppleToOrangeRatio times the number of apple juice boxes as the number of orange juice boxes. However, he must also drink at least MinOrangeJuice boxes of orange juice. To avoid a vitamin C overdose, the scientist can consume at most MaxVitaminC units of vitamin C. The objective is to determine the number of each type of juice box the scientist should drink to maximize his total vitamin D intake.


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A cleaning company uses a cleansing chemical and odor-removing chemical to clean a house. Each unit of the cleansing chemical takes CleansingTimePerUnit to be effective while each unit of the odor-removing chemical takes OdorRemovingTimePerUnit to be effective. The company must use at least MinCleansingChemical of the cleansing chemical. In total, at least MinTotalChemicals of chemicals must be used per house. Further, because the cleansing chemical is strong, there can be at most MaxCleansingToOdorRatio times the amount of odor-removing chemical as cleansing chemical. The objective is to determine the number of units of each chemical to minimize the total time it takes for a house to be cleaned.


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A drug company is producing two types of pills: allergy pills and fever reducing pills, using two factories: factory 1 and factory 2. Factory 1 produces AllergyPillsPerHourFactory1 allergy pills and FeverPillsPerHourFactory1 fever reducing pills per hour, requiring CompoundPerHourFactory1 units of a rare compound per hour. Factory 2 produces AllergyPillsPerHourFactory2 allergy pills and FeverPillsPerHourFactory2 fever reducing pills per hour, requiring CompoundPerHourFactory2 units of the rare compound per hour. The company has TotalCompoundAvailable units of the rare compound available. The company must produce at least MinAllergyPills allergy pills and MinFeverPills fever reducing pills. The objective is to determine the number of hours each factory should operate to minimize the total operating time while satisfying all constraints.


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A clinic takes patient blood pressure either using an automatic machine or a manual machine. The automatic machine takes TimeAutomatic per patient while the manual machine takes TimeManual per patient. Since the automatic machine frequently breaks, at least ManualToAutomaticRatio times the number of patients processed by the automatic machine must have their blood pressure taken by the manual machine. However, at least MinPatientsAutomatic patients can be processed by the automatic machine. If the clinic is open for TotalTime, maximize the number of patients whose blood pressure can be taken.


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A patient with a sore throat can drink NumSyrups different syrups for treatment. Each serving of syrup i delivers MedicineToThroat[i] units of medicine to the throat and MedicineToLungs[i] units of medicine to the lungs. Furthermore, each serving of syrup i contains SugarContent[i] units of sugar. The patient can get at most MaxMedicineThroat units of medicine for the throat and at least MinMedicineLungs units of medicine to the lungs. How many servings of each syrup should the patient take to minimize their sugar intake?


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A science show performs NumDemos different demonstrations. Demonstration i requires MintRequirement[i] units of mint and ActiveRequirement[i] units of active ingredient to produce MintyFoamProduced[i] units of minty foam. Additionally, demonstration i produces BlackTarProduced[i] units of black tar. The show has AvailableMint units of mint and AvailableActive units of active ingredient available. The maximum allowable production of black tar is MaxBlackTar units. The task is to determine the optimal number of each demonstration to maximize the total amount of minty foam produced, without exceeding the available resources and the maximum allowable black tar.


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A parent feeds their baby two flavors of baby food, apple and carrot, in order to meet the baby's fat and folate requirements. Each serving of apple flavored baby food contains FatPerAppleServing units of fat and FolatePerAppleServing units of folate. Each serving of carrot flavored baby food contains FatPerCarrotServing units of fat and FolatePerCarrotServing units of folate. The baby does not like the carrot flavor, and therefore he must eat AppleCarrotConsumptionRatio times as many apple flavored baby food servings as carrot flavored baby food servings. However, he must eat at least MinCarrotServings servings of carrot flavored baby food. If the baby can consume at most MaxFolate units of folate, how many servings of each should he eat to maximize his fat intake?


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A pharmacy has NumFactories factories, where they make NumProducts different products. Each factory produces ProductionRate of each product per hour. Each factory also requires BaseGelRequirement units of base gel per hour. The pharmacy has AvailableBaseGel units of base gel available. Further, they must make at least MinProduction of each product. The goal is to determine how many hours each factory should be run to meet the minimum production requirements and minimize the total time needed.


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A man needs to consume at least a minimum required number of units of fat (RequiredFat) and a minimum required number of calories (RequiredCalories) by eating burgers and slices of pizza. Each burger contains given units of fat (FatPerBurger), calories (CaloriesPerBurger), and cholesterol (CholesterolPerBurger). Each slice of pizza contains given units of fat (FatPerPizza), calories (CaloriesPerPizza), and cholesterol (CholesterolPerPizza). He needs to consume at least twice as many slices of pizza as burgers (PizzaToBurgerRatio) and wants to minimize his cholesterol intake.


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A clinic makes two types of vitamin batches: shots and pills. Each batch of vitamin shots requires UnitCShots units of vitamin C and UnitDShots units of vitamin D. Each batch of vitamin pills requires UnitCPills units of vitamin C and UnitDPills units of vitamin D. The number of batches of vitamin pills (NumBatchesPills) must be larger than the number of batches of vitamin shots (NumBatchesShots). The clinic can make at most UpperLimitBatchesShots batches of vitamin shots. The clinic has AvailableC units of vitamin C and AvailableD units of vitamin D. Each batch of vitamin shots supplies SupplyShots people and each batch of vitamin pills supplies SupplyPills people. The goal is to determine the number of batches of each type (NumBatchesShots and NumBatchesPills) to maximize the number of people that can be supplied.


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A doctor's office takes the temperature of patients one by one either by using an electronic or regular thermometer. The electronic thermometer takes ElectronicThermometerTime to make a reading while the regular thermometer takes RegularThermometerTime to make a reading. Since the electronic thermometer is more accurate, at least MinElectronicRegularRatio times as many patients should have their temperature checked by the electronic thermometer than the regular thermometer. Since the electronic thermometer has a cooldown time, at least MinRegularPatients patients should have their temperature checked by a regular thermometer. If the office is open for TotalOpenTime, maximize the total number of patients whose temperature is taken.


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A patient can be hooked up to two machines to have medicine delivered, machine 1 and machine 2. Machine 1 delivers MedicineDeliveryRateMachine1Heart units of medicine to the heart per minute and MedicineDeliveryRateMachine1Brain units of medicine per minute to the brain. Machine 2 delivers MedicineDeliveryRateMachine2Heart units of medicine per minute to the heart and MedicineDeliveryRateMachine2Brain units of medicine per minute to the brain. In addition however, machine 1 creates WasteProductionRateMachine1 units of waste per minute while machine 2 creates WasteProductionRateMachine2 units of waste per minute. If at most MaxMedicineHeart units of medicine can be received by the heart and at least MinMedicineBrain units of medicine should be received by the brain, how many minutes should each machine be used to minimize the total amount of waste produced?


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A travelling salesman consumes packs of ramen and fries. Each pack of ramen provides RamenCalories, RamenProtein, and RamenSodium. Each pack of fries provides FriesCalories, FriesProtein, and FriesSodium. The salesman has NumMeals meals, and at most MaxRamenPercentage of these meals can be ramen. The salesman needs to consume at least MinCalories and MinProtein in total across all meals and seeks to minimize his sodium intake.


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A science store produces two types of boxes, a cheap box and an expensive box. Each cheap box requires MetalCheapBox units of metal and AcidCheapBox units of acid to produce FoamCheapBox units of foam, while giving off HeatCheapBox units of heat. Each expensive box requires MetalExpensiveBox units of metal and AcidExpensiveBox units of acid to produce FoamExpensiveBox units of foam, while giving off HeatExpensiveBox units of heat. The store has TotalMetal units of metal and TotalAcid units of acid available. The total heat given off by the boxes cannot exceed MaxHeat units. The objective is to determine the number of each type of box to produce in order to maximize the total foam produced.


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A woman eats servings of almonds and servings of cashews to meet her weekly intake of MinimumCalories calories and MinimumProtein grams of protein. A serving of almonds provides CaloriesAlmonds calories, ProteinAlmonds grams of protein, and FatAlmonds grams of fat. A serving of cashews provides CaloriesCashews calories, ProteinCashews grams of protein, and FatCashews grams of fat. The woman must consume at least MinimumAlmondCashewRatio times as many servings of almonds as cashews. The objective is to determine the number of servings of almonds and cashews she should eat to minimize her fat intake.


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A company makes LiquidSanitizer and FoamSanitizer. Each LiquidSanitizer requires WaterLiquidSanitizer units of water and AlcoholLiquidSanitizer units of alcohol. Each FoamSanitizer requires WaterFoamSanitizer units of water and AlcoholFoamSanitizer units of alcohol. The company has TotalWater units of water and TotalAlcohol units of alcohol available. The number of FoamSanitizer made must be greater than the number of LiquidSanitizer. Additionally, at most MaxLiquidSanitizer units of LiquidSanitizer can be made. Each LiquidSanitizer can clean HandsCleanedByLiquid hands and each FoamSanitizer can clean HandsCleanedByFoam hands. The objective is to determine the number of LiquidSanitizer and FoamSanitizer to produce to maximize the total number of hands that can be cleaned.


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A patient in the hospital can take two different pain killers, pain killer 1 and pain killer 2. Per dose, pain killer 1 delivers LegsMedicinePainKiller1 units of medicine to the legs and BackMedicinePainKiller1 units of medicine to the back. Per dose, pain killer 2 delivers LegsMedicinePainKiller2 units of medicine to the legs and BackMedicinePainKiller2 units of medicine to the back. In addition, pain killer 1 delivers SleepMedicinePainKiller1 units of sleeping medicine and pain killer 2 delivers SleepMedicinePainKiller2 units of sleeping medicine. At most MaxSleepMedicine units of sleeping medicine should be delivered, and at least MinLegsMedicine units of medicine should be delivered to the legs. The goal is to determine the number of doses of each pain killer that should be taken to maximize the amount of medicine delivered to the back.


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A pharmaceutical company has TotalPainkillerMedicine units of painkiller medicine and makes daytime and nighttime painkiller pills. A daytime pill has PainkillerInDaytimePill units of painkiller medicine and SleepMedicineInDaytimePill units of sleep medicine. A nighttime pill has PainkillerInNighttimePill units of painkiller medicine and SleepMedicineInNighttimePill units of sleep medicine. Since some people don’t want the sleeping effect, at least MinPercentageDaytimePills percent of the pills must be daytime pills. However at least MinNighttimePills nighttime pills must be made. The objective is to determine the number of each pill that should be made to minimize the total amount of sleep medicine required.


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A competitive eater challenges himself to eat slices of cheesecake and caramel cake. Each slice of cheesecake contains CaloriesCheesecake and SugarCheesecake. Each slice of caramel cake contains CaloriesCaramelCake and SugarCaramelCake. He prefers cheesecake and decides to eat at least MinCheesecakeRatio times as many slices of cheesecake as there are slices of caramel cake. However, he must also eat at least MinCaramelSlices slices of caramel cake. If he can consume at most MaxCalories in one day, how many slices of each cake should he eat to maximize the total amount of sugar he consumes?


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A patient needs to determine the optimal number of oranges and grapefruits to eat in order to minimize their sugar intake. One orange contains VitCOranges units of vitamin C, VitAOranges units of vitamin A, and SugarOranges grams of sugar. One grapefruit contains VitCGrapefruit units of vitamin C, VitAGrapefruit units of vitamin A, and SugarGrapefruit grams of sugar. The patient must get at least MinVitC units of vitamin C and MinVitA units of vitamin A. Additionally, the patient must consume at least 2 times as many oranges as grapefruits.


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A patient is undergoing radiation treatment involving two beams, Beam1 and Beam2. Beam1 delivers DoseBeam1Pancreas units of medicine per minute to the benign area of the pancreas and DoseBeam1Skin units of medicine per minute to the benign area of the skin. Beam2 delivers DoseBeam2Pancreas units of medicine per minute to the benign area of the pancreas and DoseBeam2Skin units of medicine per minute to the benign area of the skin. In addition, Beam1 delivers DoseBeam1Tumor units of medicine per minute to the tumor and Beam2 delivers DoseBeam2Tumor units of medicine per minute to the tumor. At most MaxDoseSkin units of medicine should be received by the skin and at least MinDoseTumor units of medicine should be delivered to the tumor. The objective is to determine how many minutes of each beam, denoted as TimeBeam1 and TimeBeam2, should be used to minimize the total radiation received by the pancreas. This requires solving an optimization problem with the constraints TimeBeam1 ≥ 0 and TimeBeam2 ≥ 0.


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A body builder buys pre prepared meals, a turkey dinner and a tuna salad sandwich. The turkey dinner contains ProteinTurkeyDinner grams of protein, CarbsTurkeyDinner grams of carbs, and FatTurkeyDinner grams of fat. The tuna salad sandwich contains ProteinTunaSandwich grams of protein, CarbsTunaSandwich grams of carbs, and FatTunaSandwich grams of fat. The bodybuilder wants to get at least MinProtein grams of protein and MinCarbs grams of carbs. In addition, because the turkey dinner is expensive, at most MaxPercentTurkeyDinner percent of the meals should be turkey dinner. How many of each meal should he eat if he wants to minimize his fat intake?


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A chemistry teacher teaches her students two experiments, experiment 1 and experiment 2. In experiment 1, RedLiquidExp1 units of the red liquid and BlueLiquidExp1 units of the blue liquid mix to create GreenGasExp1 units of green gas. In experiment 2, RedLiquidExp2 units of the red liquid and BlueLiquidExp2 units of the blue liquid mix to create GreenGasExp2 units of green gas. In addition, experiment 1 produces SmellyGasExp1 units of smelly gas while experiment 2 produces SmellyGasExp2 units of smelly gas. The lab has available TotalRedLiquid units of red liquid and TotalBlueLiquid units of blue liquid. If at most MaxSmellyGas units of smelly gas can be produced, how many experiments of each should be done to maximize the total amount of green gas produced?


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A drug company is making pain killers and sleeping pills using two processes, Process1 and Process2. Process1 produces PainKillers1 units of pain killers and SleepingPills1 units of sleeping pills per hour. Process2 produces PainKillers2 units of pain killers and SleepingPills2 units of sleeping pills per hour. Process1 requires Material1 units of preliminary material while Process2 requires Material2 units of preliminary material. The drug company has AvailableMaterial units of preliminary material and must produce at least MinPainKillers units of pain killers and MinSleepingPills units of sleeping pills. The goal is to determine how many hours each of Process1 and Process2 should be run to meet the production requirements while minimizing the total hours of operation.


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A dietician recommends her client eat blueberries and strawberries to meet her anti-oxidant and mineral requirement. A pack of blueberries contains AntioxidantsBlueberries units of anti-oxidants and MineralsBlueberries units of minerals. A pack of strawberries contains AntioxidantsStrawberries units of anti-oxidants and MineralsStrawberries units of minerals. The client must get at least MinAntioxidants units of anti-oxidants and MinMinerals units of minerals. In addition, because blueberries are not in season, the dietician recommends she eats at least MinRatioStrawberriesBlueberries times as many packs of strawberries as blueberries. If a pack of blueberries contains SugarBlueberries grams of sugar and a pack of strawberries contains SugarStrawberries grams of sugar, how many packs of each should she consume to minimize her sugar intake?


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A company can transport their boxes using their own vans or by renting trucks. Their vans can transport BoxesPerVan per trip while a truck can transport BoxesPerTruck per trip. Since they own their vans, the cost per van trip is CostPerVan while the cost per truck trip is CostPerTruck. The company needs to transport at least MinBoxes and they have a budget of MaxBudget. Since the vans also provide advertising, the number of trips by van must be larger than the number of trips by trucks. How many trips by each should be done to minimize the total number of trips?


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A farmer transports his honey in two types of bottles, small and large. A small bottle has a capacity of SmallBottleCapacity units of honey while a large bottle has a capacity of LargeBottleCapacity units of honey. There are at most MaxSmallBottles small bottles and MaxLargeBottles large bottles available. The farmer must use at least twice as many small bottles as large bottles. Additionally, the total number of bottles used must not exceed MaxTotalBottles, and at least MinLargeBottles bottles must be large. The objective is to determine the number of each type of bottle to use to maximize the total amount of honey transported.


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An international goods exporter uses ships and planes to transport goods. A ship can take ShipCapacity containers worth of goods and uses ShipFuel liters of fuel per trip. A plane can take PlaneCapacity containers worth of goods and uses PlaneFuel liters of fuel per trip. The company needs to transport at least MinContainers containers worth of goods. In addition, there can be at most MaxPlaneTrips plane trips made and a minimum of MinShipPercentage fraction of the trips must be made by ship. How many of each trip should be made to minimize the total amount of fuel consumed?


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The objective is to minimize the total amount of time needed to transport a certain number of ducks using two transportation methods: boats and canoes. Each boat can take BoatDucksPerTrip ducks per trip and takes BoatTripTime minutes per trip. Each canoe can take CanoeDucksPerTrip ducks per trip and takes CanoeTripTime minutes per trip. There is a maximum limit of MaxBoatTrips boat trips allowed, and at least MinCanoeTripPercentage percent of the total trips should be by canoe. Additionally, at least MinDucksToShore ducks need to be taken to shore.


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A soda company sends bottles of their soda to stores around the city in old and new vans. An old van can take CapacityOldVan soda bottles while a new van can take CapacityNewVan soda bottles. An old van produces PollutionOldVan units of pollution while a new van only produces PollutionNewVan units of pollution. The company needs to send at least MinBottles bottles. In addition, at most MaxNewVans new vans can be used. How many of each van should be used to minimize the total amount of pollution produced?


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A lawn mowing service provides neighborhood services using small teams and large teams. A small team requires EmployeesPerSmallTeam employees and can mow AreaSmallTeam sq ft of lawn. A large team requires EmployeesPerLargeTeam employees and can mow AreaLargeTeam sq ft of lawn. The company has TotalEmployees employees available. The number of small teams must be at least SmallTeamsFactor times the number of large teams. There must be at least MinLargeTeams large teams and at least MinSmallTeams small teams. How many of each team type should be used to maximize the amount of lawn that can be mowed?


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An aquarium conducts shows using otters and dolphins. Each otter performs OtterTricks tricks and requires OtterTreats treats to do so. Each dolphin performs DolphinTricks trick and requires DolphinTreats treats to do so. Considering the popularity, at least MinDolphins dolphins must be used, and no more than MaxOtterPercentage of the performers can be otters. With a total of TotalTreats treats available, the task is to maximize the total number of tricks that can be performed.


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An oil and gas company is sending their oil to the port using containers and trucks. A container can hold ContainerCapacity units of oil while a truck can hold TruckCapacity units of oil. Due to government restrictions, the number of trucks used has to be at most MaxTruckContainerRatio times the number of containers used. If at least MinOilRequired units of oil need to be sent to the port and at least MinContainers containers need to be used, the objective is to minimize the total number of containers and trucks used.


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A school is organizing a field trip and plans to hire buses of two types. One type of bus has a capacity of SmallBusCapacity students, and the other type has a capacity of LargeBusCapacity students. The school needs to provide transportation for at least MinStudents students. In addition, no more than a fraction MaxLargeBusPercentage of the total number of hired buses can be large buses. The objective is to determine the number of each type of bus to hire to minimize the total number of buses.


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A meat shop ships their burger patties using refrigerated trucks and vans. Each truck can take TruckCapacity patties at a cost of TruckCost per trip. Each van can take VanCapacity patties at a cost of VanCost per trip. The number of trucks must not exceed the number of vans. The meat shop has to ship at least MinPatties patties and they have a maximum budget of MaxBudget. How should they plan their shipment to minimize the total number of trips?


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A florist transports his flowers to stores in small bouquets and large bouquets. Each small bouquet has SmallBouquetFlowers flowers while each large bouquet has LargeBouquetFlowers flowers. The florist can transport at most MaxSmallBouquets small bouquets and MaxLargeBouquets large bouquets. In total, he can transport at most MaxTotalBouquets bouquets, and he must transport at least MinLargeBouquets large bouquets. Additionally, he must transport at least SmallLargeRatio times the number of large bouquets as small bouquets. The goal is to determine the number of each bouquet type he should transport to maximize the total number of flowers that reach the stores.


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A toy store decides to deliver gifts using two shipping companies: a new company and an old company. The new company can deliver NewCompanyGiftCapacity gifts per trip, while the old company can deliver OldCompanyGiftCapacity gifts per trip. The new company uses NewCompanyDieselUsage liters of diesel per trip, while the old company uses OldCompanyDieselUsage liters of diesel per trip. The toy store needs to deliver at least MinGiftsRequired gifts. The new company can make at most MaxNewCompanyTrips trips. To ensure the old company does not go out of business, at least MinOldCompanyTripPercentage of all trips must be made by the old company. The goal is to determine how many trips each company should make to minimize the total amount of diesel used.


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A zoo needs to transport TotalMonkeys to the vet either by bus or by car. A bus can transport MonkeysPerBusTrip per trip and takes TimePerBusTrip. A car can transport MonkeysPerCarTrip per trip and takes TimePerCarTrip. There can be at most MaxBusTrips. In addition, since the monkeys get aggressive when there are too many in one place, at least MinCarTripPercentage of the trips should be by car. If the zoo needs to transport TotalMonkeys, how many trips of each should be done to minimize the total time required to transport the monkeys?


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A farmer decides to move NumCows to a nearby farm using helicopters and trucks. A helicopter can take HelicopterCapacity cows per trip and creates HelicopterPollution units of pollution. A truck can take TruckCapacity cows per trip and creates TruckPollution units of pollution. The farmer only has enough money for at most MaxTruckTrips truck trips. The objective is to minimize the total amount of pollution produced while transporting NumCows.


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A meal service company delivers meals to customers either on electric bikes or scooters. A bike can hold MealsPerBike meals and requires ChargePerBike units of charge. A scooter can hold MealsPerScooter meals and requires ChargePerScooter units of charge. Since the city is more friendly towards scooters, at most MaxPercentageBikes percentage of the electric vehicles can be bikes and at least MinScooters scooters must be used. If the company only has TotalCharge units of charge available, how many of each vehicle should be used to maximize the number of meals that can be delivered?


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A car manufacturer ships their cars on large and small planes. A large plane can carry CarsPerLargePlane cars while a small plane can carry CarsPerSmallPlane cars. To reduce pollution, the number of large planes must be less than the number of small planes. The manufacturer wants to deliver at least TotalCars cars while minimizing the total number of planes used.


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A mine sends ore to the surface in small and large wagons. A small wagon holds SmallWagonCapacity units of ore while a large wagon holds LargeWagonCapacity units of ore. To avoid taking up too much space on the ramps, the number of small wagons must be at least MinRatioSmallToLarge times the number of large wagons. In addition, at least MinLargeWagons large wagons must be used. If TotalOre units of ore need to be taken to the surface, minimize the total number of wagons needed.


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A theme park transports its visitors around the park either by scooter or rickshaw. A scooter can carry ScooterCapacity people while a rickshaw can carry RickshawCapacity people. To avoid excessive pollution, at most MaxRickshawProportion of the vehicles used can be rickshaws. If the park needs to transport at least MinVisitors visitors, minimize the total number of scooters used.


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A company delivers their packages using two types of animals. One type of animal can carry PackagesPerCamel packages and requires FoodPerCamel units of food. The other type of animal can carry PackagesPerHorse packages and requires FoodPerHorse units of food. The company needs to deliver at least MinPackages packages and has TotalFood units of food available. Additionally, the number of the second type of animal cannot exceed the number of the first type of animal. The goal is to determine how many of each animal to use in order to minimize the total number of animals.


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A mail delivery service in an island village delivers mail by regular and speed boats. A regular boat can carry MailCapacityRegular pieces of mail per trip and uses GasUsageRegular liters of gas. A speed boat can carry MailCapacitySpeed pieces of mail per trip and uses GasUsageSpeed liters of gas. There can be at most MaxRegularTrips regular boat trips. Since customers want their mail as fast as possible, at least MinSpeedBoatTripPercentage percent of the trips must be made by speed boats. If the service needs to deliver TotalMail pieces of mail, how many trips of each should be made to minimize the total amount of gas consumed?


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A chicken farmer needs to transport TotalChicken using either buses or cars. A bus can carry BusCapacity and takes BusTimePerTrip hours per trip. A car can carry CarCapacity and takes CarTimePerTrip hours per trip. There can be at most MaxBusTrips and at least MinCarTripPercentage of the trips must be by car. The farmer needs to determine the number of trips by car and bus to minimize the total transportation time.


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Children can go to school either by van or by minibus. A van can take VanCapacity kids and produces VanPollution units of pollution. A minibus can take MinibusCapacity kids and produces MinibusPollution units of pollution. There are at least NumChildren kids that need to go to school and at most MaxMinibuses minibuses can be used. In addition, the number of vans used must exceed the number of minibuses.


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A farmer needs to send at least MinCornWeight of corn to the city using either tractors or cars. A tractor can carry TractorCapacity of corn, and a car can carry CarCapacity of corn. The number of cars used has to be at least CarToTractorRatio times the number of tractors used. The objective is to minimize the total number of tractors and cars needed.


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A village provides bike and car transportation for everyone. A bike can take PeoplePerBike people while a car can take PeoplePerCar people. Since cars are more expensive, at most MaxPercentageCars of the vehicles can be cars. If the village needs to transport at least MinPeople people, how many of each vehicle should be used to minimize the total number of bikes needed?


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A water salesman collects water from a glacier and transports it in either small or large kegs. A small keg can hold SmallKegCapacity liters of water while a large keg can hold LargeKegCapacity liters of water. The salesman has available at most MaxSmallKegs small kegs and MaxLargeKegs large kegs. Since small kegs are easier to carry, at least MinSmallToLargeRatio small kegs must be used for every large keg. If he can transport at most MaxTotalKegs kegs total and at least MinLargeKegs kegs must be large, how many of each should he use to maximize the total amount of glacial water he can transport?


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A city needs to transport at least TotalMail pieces of mail using either submarines or boats. A submarine can carry SubmarineCapacity pieces of mail per trip and uses SubmarineGasUsage liters of gas per trip. A boat can carry BoatCapacity pieces of mail per trip and uses BoatGasUsage liters of gas per trip. The maximum allowable trips by submarine is MaxSubmarineTrips. At least MinBoatTripPercentage of the trips must be made by boat. The objective is to determine the number of submarine trips and boat trips that minimize the total gas usage while meeting these constraints.


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The weather is freezing and the fish in the pond need to be transported either by helicopter or car. A helicopter can take HelicopterFishCapacity fish per trip and takes HelicopterTripTime minutes. A car can take CarFishCapacity fish per trip and takes CarTripTime minutes. Since helicopter trips are expensive, there can be at most MaxHelicopterTrips helicopter trips. In addition, at least MinCarTripPercentage of the trips should be by car. If at least MinFishRequired fish need to be transported, how many of each trip should be taken to minimize the total time needed?


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A tourist spot in the mountains allows visitors to travel to the top either by hot-air balloon or gondola lift. A hot air balloon can carry BalloonCapacity visitors while a gondola lift can carry GondolaCapacity visitors. Each hot air balloon produces BalloonPollution units of pollution while each gondola lift produces GondolaPollution units of pollution. There can be at most MaxBalloons hot-air balloon rides and at least MinVisitors visitors need to be transported. How many of each type of transport method should be taken to minimize the total pollution produced?


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A factory transports rice to the city in horse-drawn carts that are either medium or large size. A medium sized cart requires HorsesPerMediumCart horses and can carry CapacityMediumCart kg of rice. A large sized cart requires HorsesPerLargeCart horses and can carry CapacityLargeCart kg of rice. The factory has NumHorses horses available. The number of medium sized carts must be MediumToLargeCartRatio times the number of large sized carts. There must be at least MinMediumCarts medium sized carts and at least MinLargeCarts large sized carts. How many of each cart size should be used to maximize the amount of rice that can be transported?


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A dog school trains labradors and golden retrievers to deliver newspapers. A labrador can deliver NewspapersPerLabrador newspapers at a time and requires TreatsPerLabrador small bone treats for service. A golden retriever can deliver NewspapersPerGoldenRetriever newspapers at a time and requires TreatsPerGoldenRetriever small bone treats per service. The school only has TotalTreats small bone treats available. In addition, at least MinGoldenRetrievers golden retrievers must be used and at most MaxLabradorPercentage of the dogs can be labradors. How many of each dog should be used to maximize the number of newspapers that can be delivered?


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A construction company in the tropics uses cows and elephants to carry bricks. A cow can carry BricksPerCow on its back while an elephant can carry BricksPerElephant on its back. To avoid having elephants create too much traffic, the number of elephants cannot exceed the number of cows. In addition, there can be at most MaxCowsToElephantsRatio times the number of cows as elephants (i.e., the maximum ratio of cows to elephants is MaxCowsToElephantsRatio). If the company needs to transport at least MinBricks, find the minimum number of animals, cows and elephants, that can be used.


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A farmer on an island sends corn to the main land either by ferry or light rail. Each ferry trip can take FerryCapacity boxes of corn while each light rail trip can take LightRailCapacity boxes of corn. Since ferry trips are slow, the number of light rail trip has to be at least LightRailToFerryRatio times the number of ferry trips. If the farmer wants to send at least MinBoxes boxes of corn, minimize the total number of trips of either type needed.


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A chemical company is transporting their hydrogen using two different methods, high pressure tube trailers and liquefied hydrogen tankers. Constants: VolumeHPTT is the volume transported per high pressure tube trailer trip. CostHPTT is the cost per high pressure tube trailer trip. VolumeLHT is the volume transported per liquefied hydrogen tanker trip. CostLHT is the cost per liquefied hydrogen tanker trip. MinVolume is the minimum volume of hydrogen to transport. Budget is the budget available for transportation. Decision Variables: NumHPTT is the number of trips done using the high-pressure tube trailers, and NumLHT is the number of trips done using the liquefied hydrogen tankers. Constraints: The total transported volume (VolumeHPTT * NumHPTT + VolumeLHT * NumLHT) must be at least MinVolume. The total cost (CostHPTT * NumHPTT + CostLHT * NumLHT) must not exceed Budget. The number of high pressure tube trailer trips (NumHPTT) must be less than the number of liquefied hydrogen tanker trips (NumLHT). Objective: Minimize the total number of trips (NumHPTT + NumLHT).


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A farmer transports his grapes in either small crates or large crates. Each small crate can take SmallCrateCapacity number of grapes while each large crate can take LargeCrateCapacity number of grapes. The customers prefer smaller crates, so the farmer must use at least MinSmallCratesToLargeCratesRatio times as many small crates as large crates. The farmer has at most MaxSmallCrates small crates and at most MaxLargeCrates large crates available. His truck can transport at most MaxTotalCrates crates in total, using at least MinLargeCrates large crates. The objective is to determine the number of small and large crates to maximize the total number of grapes transported.


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Patients need to be transported to the hospital by either a helicopter or a bus. A helicopter can transport HelicopterCapacity patients per trip and takes HelicopterTripTime hours. A bus can transport BusCapacity patients per trip and takes BusTripTime hours. At least MinPatientsToTransport patients need to be transported and at least MinHelicopterTripPercentage percent of the trips should be by helicopter. Additionally, there can be at most MaxBusTrips bus trips. The objective is to minimize the total time to transport the patients.


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Employees have the option of car-pooling to work or taking the company bus. A car can take CarCapacity employees and produces CarPollution units of pollution, while a bus can take BusCapacity employees and produces BusPollution units of pollution. At least NumEmployees employees need to be transported and a maximum of MaxBuses buses can be used. How many of each type of transport should be taken to minimize the total pollution produced.


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A company removes snow using two types of trucks: small trucks and large trucks. Let NumSmallTrucks represent the number of small trucks and NumLargeTrucks represent the number of large trucks. A small truck requires PeopleForSmallTruck people to shovel the snow and can carry CapacitySmallTruck units of snow. A large truck requires PeopleForLargeTruck people to shovel the snow and can carry CapacityLargeTruck units of snow. The company has a total of TotalPeople available. At least MinSmallTrucks small trucks are required. At least MinLargeTrucks large trucks are required. Additionally, the number of small trucks (NumSmallTrucks) must be twice the number of large trucks (NumLargeTrucks). The goal is to determine the number of each type of truck to use in order to maximize the total amount of snow transported.


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A magic school sends letters to students either by carrier pigeons or owls. A carrier pigeon can carry CarrierPigeonCapacity letters at a time and requires CarrierPigeonTreats treats for service. An owl can carry OwlCapacity letters at a time and requires OwlTreats treats for service. At most MaxOwlPercentage of the birds can be owls. In addition, the school only has NumTreats treats available and at least MinCarrierPigeons carrier pigeons must be used. How many of each bird can be used to maximize the total number of letters that can be sent.


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A large fishing boat sends fish back to shore either by small canoes or smaller diesel boats. A small canoe can carry back CapacityCanoe fish while a small diesel boat can carry back CapacityDieselBoat fish. In order to follow environmental rules, the number of small canoes used has to be at least CanoeToDieselRatio times the number of diesel boats used. If at least MinFish fish need to be transported to shore, minimize the total number of canoes and diesel boats needed.


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A company needs to provide a diet that meets at least MinCalories calories, MinProtein grams of protein, and MinCarbs grams of carbs for its workers. One type of food, referred to as a hamburger, costs HamburgerCost and contains HamburgerCalories calories, HamburgerProtein grams of protein, and HamburgerCarbs grams of carbs. Another type of food, referred to as a chicken wrap, costs ChickenWrapCost and contains ChickenWrapCalories calories, ChickenWrapProtein grams of protein, and ChickenWrapCarbs grams of carbs. The objective is to find the minimum cost combination of these foods that meets the dietary requirements.


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A company makes NumProducts different products. Each product i requires AssemblyTime[i] of assembly and SandingTime[i] of sanding. The company has available AvailableAssemblyTime for assembly and AvailableSandingTime for sanding. The profit per unit of product i is Profit[i]. How many of each product should the company make to maximize profit?


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A young boy wants to get a minimum of MinCalcium units of calcium and MinIron units of iron per day. A glass of milk costs CostMilk and contains CalciumMilk units of calcium and IronMilk units of iron. A plate of vegetables costs CostVegetables and contains CalciumVegetables units of calcium and IronVegetables units of iron. The goal is to determine the number of glasses of milk and plates of vegetables he should consume to minimize his cost.


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Bob wants to design a diet consisting of two types of food items. Assume that the first food item costs CostNoodles per serving and contains CaloriesNoodles calories and ProteinNoodles grams of protein. Assume that the second food item costs CostProteinBar per serving and contains CaloriesProteinBar calories and ProteinProteinBar grams of protein. Bob is interested in minimizing the cost of his diet while ensuring that his meals provide at least MinCalories calories and at least MinProtein grams of protein per day.


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An individual takes two different supplements to satisfy daily iron and calcium requirements. Each pill of the first supplement contains IronInSupplementA units of iron and CalciumInSupplementA units of calcium. Each pill of the second supplement contains IronInSupplementB units of iron and CalciumInSupplementB units of calcium. The individual needs at least MinIronRequirement units of iron and at least MinCalciumRequirement units of calcium per day. The cost per pill of the first supplement is PriceSupplementA, and the cost per pill of the second supplement is PriceSupplementB. The objective is to determine the number of pills of each supplement the individual should take to minimize the total cost while meeting the daily iron and calcium requirements.


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A woman has TotalMoney to gamble on three sports bets: a basketball tournament, a horse race, and a soccer game. Based on simple analysis, the woman determines her chance of losing her money would be ProbLoseBasketball for the basketball tournament, ProbLoseHorseRace for the horse race, and ProbLoseSoccer for the soccer game. The payout for each dollar put on each bet will be PayoutBasketball for the basketball tournament, PayoutHorseRace for the horse race, and PayoutSoccer for the soccer game. She limits her average chance of losing her money to at most MaxAvgProbLose. The goal is to determine the amount of money to put on each sport bet to maximize her expected payout.


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A repairman fixes two types of appliances. Each appliance of the first type (washing machine) takes InspectionTimeWashingMachine for inspection and FixingTimeWashingMachine for fixing. Each appliance of the second type (freezer) takes InspectionTimeFreezer for inspection and FixingTimeFreezer for fixing. The repairman has AvailableInspectionTime for inspection and AvailableFixingTime in his schedule. If each appliance of the first type repaired earns him EarningWashingMachine and each appliance of the second type repaired earns him EarningFreezer, how many of each appliance should he fix to maximize his earnings?


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A bakery has TotalBatter of batter and TotalMilk of milk to make their crepe cakes, sponge cakes, and birthday cakes. A crepe cake needs BatterCrepeCake of batter and MilkCrepeCake of milk. A sponge cake requires BatterSpongeCake of batter and MilkSpongeCake of milk. A birthday cake requires BatterBirthdayCake of batter and MilkBirthdayCake of milk. If the profit per crepe cake is ProfitCrepeCake, the profit per sponge cake is ProfitSpongeCake, and the profit per birthday cake is ProfitBirthdayCake, how many of each should the bakery make to maximize their profit?


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Super Shop sells two types of snacks in bulk: cat paw snacks and gold shark snacks. It plans to create two mix products. The first mix contains PercentCatPawFirstMix of cat paw snacks and PercentGoldSharkFirstMix of gold shark snacks. The second mix contains PercentCatPawSecondMix of cat paw snacks and PercentGoldSharkSecondMix of gold shark snacks. The store has AvailableCatPawSnacks of cat paw snacks and AvailableGoldSharkSnacks of gold shark snacks on hand. The profit per kilogram of the first mix is ProfitFirstMix and the profit per kilogram of the second mix is ProfitSecondMix. The objective is to determine how many kilograms of each mix should be prepared to maximize profit.


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A company sells two types of subscription software packages: a personal license and a commercial license which will cost CostPersonalLicense and CostCommercialLicense to generate respectively. The marketing department estimates that they can sell at most MaxLicenses licenses for both versions combined a month. The profit per personal license is ProfitPersonalLicense and the profit per commercial license is ProfitCommercialLicense. If the company does not want to spend more than BudgetLimit, how many of each software package should they produce to maximize the profits.


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The government is reworking pipes to transport water to houses. Water can be transported through wide pipes or narrow pipes. Wide pipes transport WidePipeFlowRate units of water per minute, and narrow pipes transport NarrowPipeFlowRate units of water per minute. The number of wide pipes can be at most WidePipeFraction the number of narrow pipes. There needs to be at least MinWaterTransport units of water transported every minute, and at least MinWidePipes wide pipes must be used. Minimize the total number of pipes required.


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A student takes pills, where each pill type has a different effectiveness time. The student must take at least TotalPills pills over a month, with at least MinVitaminDPills of them being vitamin D pills. The effectiveness times for calcium and vitamin D pills are CalciumTime and VitaminDTime respectively. The student must also take more calcium pills than vitamin D pills. The goal is to determine the number of each type of pill to take in order to minimize the total effectiveness time sum of all pills taken.


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An amusement park has two types of games: throwing and climbing games. Throwing games attract ThrowingGameCustomers customers every hour and climbing games attract ClimbingGameCustomers customers every hour. Throwing games cost the amusement park ThrowingGameCost in prizes per hour whereas climbing games cost ClimbingGameCost in prizes per hour. Since throwing games yield the most profit, there must be at least ThrowingToClimbingRatio times as many throwing games as climbing games. However, at least MinClimbingGames games must be climbing games. If the amusement park can have at most MaxPrizeCost in prizes every hour, maximize the total number of customers attracted every hour.


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Determine the quantity of circular and rectangular tables to set up at a science fair in order to maximize the number of catered guests. Each circular table fits PosterBoardsCircular poster boards and ParticipantsCircular participants, catering to GuestsCircular guests and taking up SpaceCircularTable units of space. Each rectangular table fits PosterBoardsRectangular poster boards and ParticipantsRectangular participants, catering to GuestsRectangular guests and taking up SpaceRectangularTable units of space. The fair must accommodate at least MinParticipants participants and MinPosterBoards poster boards, without exceeding the TotalAvailableSpace units of space.


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An oil and gas company has two types of pipes, a high-volume and a low-volume one. Every day, the high-volume pipe allows a throughput of HighVolumePipeThroughput and it is recommended that TechniciansPerHighVolumePipe technicians closely monitor the pipes to ensure that it is functioning properly. Each day, the low-volume pipe allows a throughput of LowVolumePipeThroughput and TechniciansPerLowVolumePipe technicians should closely monitor for safety reasons. Every day, the oil and gas company needs to meet the demands of at least MinimumDailyDemand of gas and they have TotalTechnicians technicians on their staff. Since the high-volume pipe has a higher risk of environmental damage, at most MaxHighVolumePipePercentage of the total number of pipes can be high-volume ones. Additionally, there must be a minimum of MinLowVolumePipes low-volume pipes. How many of each pipe types should be used to reduce the total number of pipes required?


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A hospital hires workers to provide ultrasound services. An ultrasound technician works TechnicianHoursPerShift hours per shift and is paid TechnicianPaymentPerShift per shift, while a graduate researcher works ResearcherHoursPerShift hours per shift and is paid ResearcherPaymentPerShift per shift. Due to regulations, there must be TechnicianToResearcherRatio times as many ultrasound technician shifts as graduate researcher shifts. The hospital requires TotalRequiredHours of ultrasound services and has a TotalBudget available. The objective is to schedule the minimum total number of workers.


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A delivery person can have shifts on either bikes or scooters. A shift on a bike delivers OrdersPerBikeShift orders, uses EnergyPerBikeShift units of energy, and brings in TipsPerBikeShift in tips because it is faster. A shift on a scooter delivers OrdersPerScooterShift orders, uses EnergyPerScooterShift units of energy, and brings in TipsPerScooterShift in tips. The delivery person has a total of TotalShifts available per month and TotalEnergy units of energy and must deliver at least MinOrders orders. Additionally, they must have at least MinScooterShifts shifts on scooters because bikes are harder to get. The goal is to determine the number of shifts on each type of transportation to maximize the tips received.


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A singer can hold two types of concerts: pop and R&B. Each pop concert brings in PopAudience audience members and requires PopPracticeDays practice days. Each R&B concert brings in RnBAudience audience members and requires RnBPracticeDays practice days. The singer must bring in at least MinAudienceRequired total audience members and has a maximum of MaxPracticeDays practice days available. Additionally, the singer can perform at most MaxRnBConcertRate of his total concerts as R&B concerts. The objective is to determine the number of each type of concert to minimize the total number of concerts.


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A neighbourhood pizza restaurant sells two sizes of pizzas: large and medium. Each large pizza requires DoughLargePizza units of dough and ToppingsLargePizza units of toppings, and takes TimeLargePizza minutes to bake. Each medium pizza requires DoughMediumPizza units of dough and ToppingsMediumPizza units of toppings, and takes TimeMediumPizza minutes to bake. The restaurant must use at least MinDough units of dough and at least MinToppings units of toppings. Due to a promotion, at least MinMediumPizza medium pizzas need to be made. To cater to regulars, the number of large pizzas should be at least LargeToMediumRatio times the number of medium pizzas, where LargeToMediumRatio represents the value 2. The objective is to minimize the total baking time.


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A restaurant can deliver their food by two methods. Servers can deliver by one method and will have CartInteractions customer interactions and will need to refill food CartRefills times per hour. They can also deliver food by another method with increased mobility, achieving HandInteractions customer interactions while needing HandRefills refills per hour. At least MinCartPercentage of delivery shifts must be by the first method. Additionally, there must be at least MinHandServers servers delivering by the second method. The restaurant aims to have TotalInteractions customer interactions per hour. Determine the number of servers for each delivery method to minimize the total number of refills per hour.


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A restaurant has two combos available to their customers: an original meal and an experimental meal. The original meal generates OriginalFoodWaste units of food waste, OriginalWrappingWaste units of wrapping waste, and takes OriginalCookingTime minutes to cook. The experimental meal generates ExperimentalFoodWaste units of food waste, ExperimentalWrappingWaste units of wrapping waste, and takes ExperimentalCookingTime minutes to cook. The restaurant must adhere to a maximum of MaxWrappingWaste units of wrapping waste and MaxFoodWaste units of food waste as regulated by the government. The goal is to determine the number of each meal to be promoted by the waiting staff to minimize the total cooking time while complying with waste constraints.


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A metal-working shop has access to two types of metal-working equipment, a chop saw and a steel cutter. A chop saw can work ChopSawCapacity of metal and generates ChopSawWaste units of waste every day. A steel cutter can work SteelCutterCapacity of metal and generates SteelCutterWaste units of waste every day. The metal-working shop must cut TotalMetalCuttingRequirement of metal every day. However, there is a waste limitation and they may at most produce MaxAllowedWaste units of waste every day. The objective is to minimize the total number of metal-working equipment needed.


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A market owner wants to start a jam business. He can either sell one unit of jam to customers in a set of small packets or jugs. A set of small packets can hold VolumeSmallPackets ml of jam while a jug can hold VolumeJug ml of jam. Since a set of small packets are more expensive to make, at least MinRatioJugToPackets times the number of jugs must be used as sets of small packets. Additionally, at least MinSetsSmallPackets sets of small packets should be filled. If the market owner has TotalVolumeJam ml of jam, how many sets of small packets or jugs should be selected to maximize the total number of units that he can sell to his customers?


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The goal is to determine the quantities of two types of meals, one denoted as 'salad' and the other as 'fruit bowl.' Each type of meal contributes different amounts of vitamins, fibres, and potassium. The objective is to maximize the total potassium intake. There are constraints to ensure a minimum required intake of vitamins and fibres: MinVitamin and MinFibre. Each salad provides VitaminPerSalad units of vitamins and FibrePerSalad units of fibre. Each fruit bowl provides VitaminPerFruitBowl units of vitamins and FibrePerFruitBowl units of fibre. Additionally, there is a constraint that at most MaxFruitBowlPercentage of the meals can be fruit bowls. Each salad contains PotassiumPerSalad units of potassium and each fruit bowl contains PotassiumPerFruitBowl units of potassium.


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A company wants to determine the number of retail stores and factory outlets to open to satisfy MinCustomersPerDay, while using at most MaxEmployees. Each retail store brings in RetailStoreCustomers and requires RetailStoreEmployees to operate. Each factory outlet brings in FactoryOutletCustomers and requires FactoryOutletEmployees to run. The goal is to minimize the number of retail stores and factory outlets that need to be open.


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A soda company needs to bottle at least MinTotalVolume of soda every day. A can holds VolumeCan of soda whereas a bottle holds VolumeBottle of soda. The number of cans must be at least MinRatioCansToBottles times the number of glass bottles, and at least MinBottles glass bottles must be produced due to contracts. How many cans and bottles should be made to maximize the total number of units produced?


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A candle-making company can move their inventory of candles using freight and air. Freight can transport TonsPerFreight tons per trip while using air can transport TonsPerAir tons per trip. Since freight takes longer, the cost for each freight trip is FreightCost while the cost over air for each trip is AirCost. The company needs to transport at least TotalTons tons of candles and they have a budget of Budget. Additionally, due to some urgent orders, at least MinAirPercentage of total tons must be transported through air. There must also be at least MinFreightTrips trips through freight. How many of trip by each should be scheduled to minimize the total number of trips?


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A production company needs to transport TotalPeople using large mobile production units or small mobile production units. Large mobile production units can hold LargeUnitCapacity people and take up LargeUnitParkingSpots parking spots whereas small mobile production units can hold SmallUnitCapacity people and take up SmallUnitParkingSpots parking spots. Movie stars prefer to have their small mobile production unit to share with a close staff, therefore at least MinSmallUnits units must be small mobile units. However, due to logistic limitations, large mobile production units are more space efficient per spot, they must make up at least MinPercentageLargeUnits of all vehicles. Minimize the total number of parking spots required by this production.


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A company ships items to stores using two different types of boxes. A small box holds MasksInSmallBox masks whereas a large box holds MasksInLargeBox masks. Since small boxes are easier to stack and will be used first to stock stores, there must be at least MinSmallToLargeRatio times as many small boxes as large boxes. Additionally, at least MinLargeBoxes large boxes must be used. If at least MinMasksRequired masks are required to be distributed, how many of each size of box should be used to minimize the total number of boxes needed?


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An autobody shop needs to purchase two types of car jacks, an automatic electric one, or a gas-powered one. The automatic electric one can process CarsPerHourElectric cars every hour and uses ElectricityPerHourElectric units of electricity whereas the gas-powered one can process CarsPerHourGas cars each hour using GasPerHourGas units of gas. Since there is a limit to how many automatic electric ones there can be due to the limited number of power outlets, the shop must use less than MaxElectricJacks automatic electric ones. The shop can use at most MaxElectricity units of electricity and MaxGas units of gas. How many of each type of jack should the shop purchase to maximize the amount of cars processed every hour?


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A railway company is planning the infrastructure for the city and is considering two types of transportation, trains and trams. Each train can transport PeoplePerTrain people comfortably per hour and each tram can transport PeoplePerTram people comfortably per hour. Since trains take longer to build, the number of trams must be at least MinTramToTrainRatio times the number of trains. The company wants to transport at least MinTotalPeople people per hour and aims to minimize the total number of transportation units.


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An automotive company is comparing NumCatalysts different catalysts. The process with catalyst i requires PlatinumRequired[i] units of platinum and PalladiumRequired[i] units of palladium and can perform the conversion to carbon dioxide at a rate of ConversionRate[i] units per second. There are TotalPlatinumAvailable units of platinum and TotalPalladiumAvailable units of palladium available. How many of each catalyst should be used to maximize the amount converted into carbon dioxide?


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There are two processes, J and P, to extract metal from ores. Process J extracts MetalExtractedJ units of metal using WaterUsedJ units of water and produces PollutionProducedJ units of pollution. Process P extracts MetalExtractedP units of metal using WaterUsedP units of water and produces PollutionProducedP units of pollution. The objective is to determine the number of times each process should be performed to maximize the total metal extracted, subject to the constraints that the total water used does not exceed MaxWater units and the total pollution produced does not exceed MaxPollution units.


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An airport needs to install either escalators or elevators to transport people. Escalators have a transport capacity of EscalatorCapacity and take up EscalatorSpace units of space. Elevators have a transport capacity of ElevatorCapacity and take up ElevatorSpace units of space. The total transport capacity of all installed escalators and elevators must be at least RequiredCapacity. Additionally, the number of escalators must be at least EscalatorElevatorRatio times the number of elevators, and at least MinElevators elevators must be used. The goal is to minimize the total units of space taken by escalators and elevators.


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A research group is making fabric and plastic using two methods, method A and method B. Method A produces FabricUnitsA units of fabric and PlasticUnitsA units of plastic per hour. Method B produces FabricUnitsB units of fabric and PlasticUnitsB units of plastic per hour. Method A requires SpecialElementA units of a special element while method B requires SpecialElementB units of the same special element. The research group has available TotalSpecialElement units of the special element and must make at least MinFabric units of fabric and MinPlastic units of plastic. How many of each method should be executed to minimize the total time needed?


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Due to an accident, at least MinLocals locals must be moved across a lake. They can either be transported over the lake by a kayak or a motorboat. Kayaks can transport KayakCapacity people per trip and motorboats can transport MotorboatCapacity people per trip. Kayaks take KayakTime minutes per trip whereas motorboats take MotorboatTime minutes per trip. Due to the limited number of motorboats available to the locals, there can be at most MaxMotorboatTrips motorboat trips and at least MinKayakTripProportion of the total trips should be by kayak. How many of each transportation method should be used to minimize the total amount of time needed to transport all the locals?


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A researcher is outsourcing annotations and has two options: a specialized third-party or a common third-party annotation company. The specialized company can annotate at a rate of SpecializedRate images per hour whereas the common company can annotate at a rate of CommonRate images per hour. However, the specialized company charges SpecializedCost per hour and the common company charges CommonCost per hour. The researcher has deadlines to meet and must complete a dataset of at least TotalImages images. They also have some special images that only the specialized company can annotate. Therefore, at least a third of the TotalImages must be allocated to the specialized company.


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A golf course is organizing an event and can transport guests using either golf carts or pull carts. Each golf cart can transport GuestsPerGolfCart guests, while each pull cart can transport GuestsPerPullCart guest. However, due to spatial constraints, at most MaxGolfCartPercentage of all carts can be golf carts. The goal is to transport at least MinGuests guests while minimizing the total number of carts used.


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A smoothie shop produces two different types of smoothies: acai berry smoothies and banana chocolate smoothies. It takes AcaiBerriesPerAcaiSmoothie units of acai berries and WaterPerAcaiSmoothie units of water to make one acai berry smoothie. It takes BananaChocolatePerBananaSmoothie units of banana chocolate and WaterPerBananaSmoothie units of water to make one banana chocolate smoothie. The number of banana chocolate smoothies made must be more than the number of acai berry smoothies made. Additionally, at least MinAcaiFraction of the total smoothies made must be acai berry smoothies. The smoothie shop has TotalAcaiBerries units of acai berries and TotalBananaChocolate units of banana chocolate. The objective is to determine the number of each type of smoothie to make in order to minimize the total amount of water used.


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A handmade sports equipment manufacturing company makes two types of sports equipment: basketballs and footballs. Basketballs require BasketballMaterial units of materials and BasketballHours hours to make, whereas footballs require FootballMaterial units of materials and FootballHours hours to make. The manufacturing company has TotalMaterial units of materials available and their workers can work for at most TotalHours hours. Since basketballs sell better, there must be at least BasketballToFootballRatio times as many basketballs as footballs, but the manufacturing company would like at least MinFootballs footballs. How many of each type of sports equipment should the manufacturing company make to maximize the total number of sports equipment produced?


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A researcher must perform two types of experiments, in-vivo and ex-vivo. In-vivo experiments require PrepTimeInVivo minutes to prepare and ExecTimeInVivo minutes to execute. Ex-vivo experiments require PrepTimeExVivo minutes to prepare and ExecTimeExVivo minutes to execute. In-vivo experiments give the researcher RadiationInVivo units of radiation while ex-vivo experiments give the researcher RadiationExVivo units of radiation. At most MaxPrepTime minutes can be used for preparation and MaxExecTime minutes for execution of the experiments. How many of each experiment should be scheduled by the researcher to minimize the total radiation received by the researcher?


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A village delivers mail to nearby villages either by runners or canoers. Runners can carry RunnerCapacity bags of mail each time and take RunnerTime hours. Canoers can carry CanoerCapacity bags of mail each time and take CanoerTime hours. At most CanoeProportion of deliveries can be by canoe. Additionally, the village can spare at most TotalHours total hours and at least MinRunners individual runners must be used. How many of each way to deliver must be used to maximize the total amount of mail that can be delivered?


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A woman on a diet needs to consume two types of meal preps. Each meal prep either provides ProteinPerSmoothie units of protein and CaloriesPerSmoothie calories, or ProteinPerBar units of protein and CaloriesPerBar calories. The woman must consume a number of protein bars equal to RatioBarsToSmoothies times the number of smoothies. She can consume at most MaxCalories calories and aims to maximize her protein intake by choosing the appropriate quantities of meal preps.


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A firm operates NumFactories factories, each producing anti-itch injections and topical cream per hour. Every hour, each factory requires a certain number of plastic units to manufacture the packaging for these products. The total available plastic units are limited, and the firm has to meet minimum production requirements for both anti-itch injections and topical cream. The objective is to determine how many hours to run each factory to minimize the total operational time while satisfying the plastic usage constraint and the production requirements for both products.


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A hospital prepares batches of medication patches and anti-biotic creams. Each medication patch requires TimePerMedPatch minutes to prepare and MaterialsPerMedPatch units of materials. Each anti-biotic cream requires TimePerCream minutes to prepare and MaterialsPerCream units of materials. Since anti-biotic creams are used more often, there must be at least MinCreamPatchRatio times as many anti-biotic creams as medication patches. Due to storage reasons, the hospital can make at most MaxTotalBatches batches of medication patches and anti-biotic creams in total. The hospital has available TotalAvailableMinutes minutes of staff to spare and TotalAvailableMaterials units of materials. If each batch of medication patches can treat PeoplePerMedPatch people and each batch of anti-biotic cream can treat PeoplePerCream people, how many batches of each should be made to maximize the number of people that can be treated?


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A company in the desert can transport goods to rural cities either by camel caravans or desert trucks. A camel caravan can deliver GoodsCamelCaravan units of goods per trip and takes HoursCamelCaravan hours. A desert truck can deliver GoodsDesertTruck units per trip and takes HoursDesertTruck hours. The company prefers to have more camel caravans than desert trucks. If the company needs to deliver TotalGoods units of goods, how many of each transportation method should be used to minimize the total number of hours required?


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Both chemical A and chemical B need to be added to a mixer for making bread. One unit of chemical A takes TimeA to be effective while one unit of chemical B takes TimeB to be effective. Because chemical A can be dangerous, there has to be at most MaxProportionAtoB as much chemical A as chemical B in the mixer. If there has to be at least MinUnitsA units of chemical A in the mixer and at least MinTotalChemicals units of total chemicals in the mixer, how many units of each should be added to minimize the total time it takes for the mixed bread to be ready?


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A senior home has snacks of spinach and soybeans to increase their intake of iron. A cup of spinach contains FibreInSpinach units of fibre and IronInSpinach mg of iron. A cup of soybeans contains FibreInSoybeans units of fibre and IronInSoybeans mg of iron. The number of cups of spinach must exceed the number of cups of soybeans due to other nutritional requirements. Additionally, a cup of spinach contains CaloriesInSpinach calories while a cup of soybeans contains CaloriesInSoybeans calories. The elderly need in total at least TotalFibreRequired units of fibre and TotalIronRequired mg of iron. How many cups of each should the nurses schedule to maximize the seniors’ total caloric intake?


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A keyboard manufacturer makes mechanical and standard keyboards. Mechanical keyboards are becoming more popular and thus the manufacturer aims to have MechanicalToStandardRatio times as many mechanical keyboards as standard keyboards. A mechanical keyboard costs PlasticPerMechanicalKeyboard units of plastic and SolderPerMechanicalKeyboard units of solder whereas a standard keyboard costs PlasticPerStandardKeyboard units of plastic and SolderPerStandardKeyboard units of solder. There are still customers that prefer a less noisy alternative. Therefore, there must be at least MinStandardKeyboards standard keyboards. If the company has available TotalPlastic units of plastic and TotalSolder units of solder, how many of each type should be manufactured to maximize the total number of keyboards?


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A dessert shop needs to decide the quantities of two desserts, matcha ice cream and orange sorbet, to minimize the total amount of flavouring used. Each order of matcha ice cream requires FlavouringMatcha units of flavouring and IceCreamMatcha units of ice cream. Each order of orange sorbet requires FlavouringOrange units of flavouring and WaterOrange units of water. The shop has AvailableIceCream units of ice cream and AvailableWater units of water. At least MinMatchaPercentage percent of the total desserts made must be matcha ice cream. Additionally, the number of orders of orange sorbet must exceed the number of orders of matcha ice cream.


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 Consider a set P described by linear inequality constraints, that is:
 P = {x \in R^N | a_i^T x <= b_i , i = 1, ..., m}.

where a_i \in R^N and b_i \in R
 A ball with center y in R^N and radius r is defined as the set of all points within (Euclidean) distance r from y.
We are interested in finding a ball with the largest possible radius, which is entirely contained within the set P (The center of such a ball is called the Chebychev center of P.


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 A quantity y is known to depend on another quantity x. A set of corresponding values has been collected for x and y and is presented. The k-th y value takes y_{k} and the k-th x value takes x_{k}.
Fit the ‘best’ straight line y = bx + a where the objective is to minimize the maximum deviation of all the observed values of y from the value predicted by the linear relationship.


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A quantity y is known to depend on another quantity x. A set of corresponding values has been collected for x and y and is presented. The k-th y value takes y_{k} and the k-th x value takes x_{k}.
Fit the ‘best’ quadratic curve y = c * x^2 + b * x + a to this set of data points. The objective is to minimize the sum of absolute deviations of each observed value of y from the value predicted by the quadratic relationship.


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 A number of power stations are committed to meeting the following electricity load demands over a day. Period t of a day has demand demand_{t}. There are several types of generating unit available: the number of k-th type units is num_{k}. Type k generator has to work between a minimum level minlevel_{k} and a maximum level maxlevel_{k}.  There is an hourly cost of running each type k generator at minimum level runcost_{k}.  In addition, there is an extra hourly cost extracost_{k} for each megawatt at which a type k unit is operated above the minimum level.  Starting up a type k generator also involves a cost startcost_{k}.
Which generators should be working in which periods of the day to minimize total cost?


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 We suppose that some products can be produced, each of them passing through several stages. Necessary time to produce 1 unit of product k is produce_time_{k, s} hours for stage s. Availability in working hours is time_{s} for stage s.  The unitary profits for product k is profit_{k}.
Determine the quantities to be produced such that all the production constraints are satisfied and the profit is maximized.


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 The knapsack problem has a significant place in the study of integer programming models with binary variables.  In the knapsack problem, one needs to pack a set of items in a container. Each item k has value value_{k} and size size_{k}. And the container has maximum capacity C.  If the total size of the items exceeds the capacity, we can't pack them all.  In that case, the problem is to choose a subset of the items of maximum total value that will fit in the container.
Maximize the total value of the packed items


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 We assume that there are available at the market different foods and that the food k sells at a price price_{k} per unit.  In addition there are several basic nutritional ingredients and, to achieve a balanced diet, each individual must receive at least demand_{m} units of nutrient m per day.  Finally, we assume that each unit of food k contains nutri_{k, m} units of nutrition m
We want to minimize the total prices of the foods to purchase.


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 Consider the problem of operating a warehouse, by buying and selling the stock of a certain commodity, in order to maximize profit over a certain length of time, say several periods. The warehouse has a fixed capacity, and there is a cost holding_cost per unit for holding stock for one period. The selling price, price_{n}$, of the commodity is known to fluctuate over a number of time periods.  In any period n the price holding for purchase is cost_{n}. The warehouse is originally empty and is required to be empty at the end of the last period.
Determine the amount of buying and selling in each period to maximize the profit over the months


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 A manufacturer wishes to produce alloy_quant lb of an alloy that consists of several kinds of metals. And by weight, the alloy we want contains a target quantitytarget_{m} of metal metal_{m}. Several other kinds of alloys are available at various prices.  These alloys can be melted to get the alloy we want. Alloy k has ratio_{k, m} ratio of metal_{m} and is sold at price of price_k. Ratio ratio_{k, m} ranges between 0 and 1.0 and should be properly treated in optimization
The manufacturer wishes to find the amounts of the various alloys needed and to determine the cheapest combination.


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 A small firm specializes in making some types of spare automobile parts.  Each part is has to go through several shops  The required worker-hours for part k in shop s is time_{k, s}. The profit of part k is profit_{k}. The capacity of shop s is capacity_{s} working hours.
Formulate the problem of determining the quantities of each spare part to be made during the month so as to maximize profit.


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 A small computer manufacturing company forecasts the demand over the next n-th month to be demand_{n}. These demands must be satisfied and can not be shorted. In any month it can produce at most max_regular_amount units, using regular production, at a cost of cost_regular dollars per unit.  By using overtime, it can produce additional units at cost_overtime dollars per unit.  The firm can store units from month to month at a cost of store_cost dollars per unit per month.
Formulate the problem of determining the production schedule that minimizes the cost.


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 To operate a cafeteria, the manager must ensure on-call duty based on the statistics on the required staff.  In the future days, the number of desired employees on day n is denoted with num_{n}. Each employee works n_working_days days in a row and then has n_resting_days days off.
Calculate the minimum number of employees to hire


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 An Italian transport company must send empty containers from its depots to ports.  The number of containers available in the depot i is denoted with numdepot_i.  Container requirement in port j is numport_{j}.  Transport of containers is by barges.  Each barge can only contain two containers and the cost of transport (per barge) is proportional to the distance traveled (price is price Euros/km). The distances between depot i and port j is distance_{i, j}.
Minimize the total transportation cost.


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 A division of an auto parts manufacturer produces P different parts using M different machines. Batch of 100 part p requires time_{m,p} hours on machine m. The division incurs a charge of cost_{m} per hour for using machine m. Machine m has an availability of up to available_{m} hours per month. The division sells part p in batches of 100 at price of price_{p} per batch. The division must produce at least min_batches_{p} batches of part p each month to fulfill a contract.
How many batches of each part should the manufacturer produce each month to maximize profit?


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 Custom Tees is planning an online advertising campaign with A different ad types across two web companies. The company has set a goal of goal_young thousand clicks from visitors aged 18-25 and goal_old thousand clicks from visitors older than 25. The company has set a goal of goal_unique_young thousand unique clicks from visitors aged 18-25 and goal_unique_old thousand unique clicks from visitors older than 25. Ad type a has an estimated percentage of young_click_{a} clicks from the 18-25 age range. Ad type a has an estimated percentage of old_click_{a} clicks from older visitors. Ad type a has a cost of cost_{a} per 1000 clicks. Ad type a has a maximum allowable clicks of max_click_{a} in thousands. The estimated percentage of unique visitors for each ad type a is unique_click_{a}.
How many clicks from each ad type should Custom Tees purchase to minimize cost?


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 A fine foods company produces gift baskets for a season that lasts W weeks. The demand for week w is demand_{w} and the demand must be met. Regular labor is available for regular_labor_{w} hours per week and costs $regular_cost/h. Overtime labor is available for overtime_labor_{w} hours per week and costs $overtime_cost/h. Each basket takes assembly_time hours of labor to assemble. The material cost for each basket is $material_cost and it sells for $selling_price. Unsold baskets from a week incur a $holding_cost holding cost.  No baskets are available at the start of week 1. Unsold baskets at the end of week W have a salvage value of $var{salvage_value} and do not incur a holding cost.
How much regular and overtime labor should be utilized each week to assemble the baskets to maximize the profit over the season?


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 A division of an auto parts manufacturer produces P different parts using M different machines. Batch of 100 part p requires time_{m,p} hours on machine m. The division incurs a charge of cost_{m} per hour for using machine m. Machine m has an availability of up to available_{m} hours per month. Machine M and Machine M-1 can share availability. Individual availability conditions for Machine M and Machine M-1 can be disregarded. The division sells part p in batches of 100 at price of price_{p} per batch. The division must produce at least min_batches_{p} batches of part p each month to fulfill a contract.
How many batches of each part should the manufacturer produce each month to maximize profit?


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 A division of an auto parts manufacturer produces P different parts using M different machines. Batch of 100 part p requires time_{m,p} hours on machine m. The division incurs a charge of cost_{m} per hour for using machine m. Machine m has an availability of up to available_{m} hours per month. The division sells part p in batches of 100 at price of price_{p} per batch. The division must produce at least min_batches_{p} batches of part p each month to fulfill a contract. Extra available time for machine m can be acquired at $extra_costs_{m}/hour.  Up to max_extra_{m} hours can be purchased for each machine m.
How many batches of each part should the manufacturer produce each month to maximize profit?


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 A team of translators is being assem- bled for the summer Olympics to translate from English into the \{M} other languages. There is a pool of N translators available. Each translator i can translate into a certain set of languages and comes with a specific cost_i.
Select the combination of translators that ensures all required languages can be translated into, at the minimum possible cost.


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A company has I projects to be done by consultants. They have a choice of J consultants. Each consultant may be assigned up to K projects.  Hiring consultant j incurs a fixed cost of f_j. Assigning project i to consultant j incurs an additional cost of c_{i,j}.
Determine the assignment of consultants to projects that minimizes the total cost.


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The network faces an intrusion that requires immediate intervention. Interventions include isolating nodes or scanning nodes affected by the intruder. Each cluster of nodes must be treated with one intervention type consistently. Interventions can be processed either centrally or through distributed nodes. The processing times for each type of intervention are different across N clusters. The opportunity cost for processing is $central_cost/h for central and $distributed_cost/h for distributed processing. There is a maximum allotment of max_central hours for central processing and max_distributed hours for distributed processing to address the intrusion.
Determine the most cost-effective combination of interventions to halt the intruder's progress within the network.


