Ch. 6.3 and Ch7.3 Applications.

Ex1) A 4-h club member raise goats and pigs. She wants to raise no more than 16 animals, including no more than 10 goats. She spends $25 to raise a goat and $75 to raise a pig, and she has $900 available for the project. Find the maximum profit she can make if each goat produces a profit of $14 and each pig a profit of $40.

Ex2) An office manager needs to purchase new filing cabinets. He knows that Ace cabinets cost $40 each, require 6 square feet of floor space, and hold 8 cubic feet of files. On the other hand, each Excello 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. How many of each type of cabinet should he buy? Ex3) Certain laboratory animals must have at least 30 grams of protein and at least 20 grams of fat per feeding period. These nutrients come from food A, which cost $.18 per unit and supplies 2 grams of protein and 4 of fat, and food B, with 6 grams of protein and 2 of fat, costing $.12 per unit. Food B is bought under a long- term contract requiring that at least 2 units of B be used per serving. How much of each food must be bought to produce the minimum cast per serving?

Ex4) The U-Drive Rent-a Truck company plans to spend $3 million on 200 new vehicles. Each van will cost $10,000, each small truck $15,000, and each large truck$25,000. Past experience shows that U-Drive needs twice as many vans as small trucks. How many of each kind of vehicle can the company buy? Ex5) Ellen plans to invest a total of $100,000 in a money market account, a bound fund, an international stock fund, and a domestic stock fund. She wants 60% of her investment to be conservative (money market and bounds). She wants the amount in international stocks to be one-fourth of the amount in domestic stocks. Finally, she needs an annual return of $4,000. Assuming she gets annual returns of 2.5% on the money market account, 3.5% on the bound fund, 5% on the international stock fund, and 6% on the domestic stock fund, how much should she put in each investment?

Ex6) Kelly sells rug-cleaning machines. The EZ model weighs 10 pounds and comes in a 10 cubic-foot box. The compact model weighs20 pounds and comes in a 8 cubic foot box. The commercial model weighs 60 pounds and comes in a 28 cubic-foot box. Each of Kelly’s delivery van has 248 cubic feet of space and can hold a maximum of 440 pounds. In order for a van to be fully loaded, how many of each model should it carry?