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Section 2.4.2 - Linear Programming……Finally PULL PACKET FROM YOUR FOLDER
A 4-H Club member raises only geese (x) and pigs (y). • She wants to raise no more than 16 animals total, including no more than 10 geese. • She spends $15 to raise a goose and $45 to raise a pig, and has $540 available for this project. • Each goose produces a profit of $6 and each pig a profit of $20. • You are trying to compute a maximum profit.
An office manager needs to purchase new filing cabinets. • He knows that Griffin (x) cabinets cost $40 each, require 6 square feet of floor space, and hold 8 cubic feet of files. • On the other hand, each Yugo (y) cabinet costs $80, requires 8 square feet of floor space, and holds 12 cubic feet. • His budget permits him to spend no more than $560 on files, while the office has room for no more than 72 square feet of cabinets. • The manager desires the greatest storage capacity within the limitations imposed by funds and space.
Certain farm animals must have at least 30 grams of protein and at least 20 grams of fat per feeding period. These nutrients come from beef (x), which costs $0.18 per unit and supplies 2 grams of protein and 4 of fat, and cereal (y), with 6 grams of protein and 2 of fat, costing $0.12 per unit. Cereal is bought under a long-term contract requiring that at least 2 units of cereal be used per serving. The goal is to keep the cost a minimum.
McDonald’s has been reserved for a special kids birthday party. • A total of 150 people will attend this party. • There will be two options for food: SUPER Happy Meal (x) and Happy Meal (y). • The manager is told that there should be at least 30 more SUPER Happy Meals available than Happy Meals and that there should be • at least 40 Happy Meals available. • The manager has to pay $3.00 for its SUPER Happy Meals and $2.00 for its Happy Meals. McDonald’s wants to minimize costs.
Apple makes two models of iPOD’s…known in the industry as ‘basic’ (x) and ‘deluxe’ (y). • The basic model requires 2 hours of assembly time and 24 square inches of material per unit; • the deluxe model requires 2 hours of assembly time and 32 square inches of material per unit. • Apple has available 600 hours of assembly time and 8,000 square inches of material per month. • The profit on the ‘basic’ model is $100 per unit and $150 on the ‘deluxe’ unit.
Target must ship at least 100 televisions to its two stores in Frankfort and Orland Park. • Each store can hold a maximum of 100 televisions. • Frankfort (x) has 25 televisions already, and Orland Park (y) has 20. • It costs $12 to ship a television to Frankfort and $10 to ship one to Orland Park. The goal is to minimize cost.
Fanny May needs to start thinking about Valentine’s Day candy. • In each store, 60 pounds of chocolate and 100 pounds of mints are available to make 5-pound boxes of candy. • A ‘regular box’ (x) has 4 pounds of chocolates and 1 pound of mints and sells for $10. • A ‘deluxe box’ (y) has 2 pounds of chocolates and 3 pounds of mints and sells for $16.