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##### Section 2.4.2 - Linear Programming……Finally

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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.