4. A diet is being prepared for the University of Arizona dorms. The objective i

Question

4. A diet is being prepared for the University of Arizona dorms. The objective is to feed the students at the least cost, but the diet must have between 1,800 and 3,600 calories. No more than 1,400 calories can be starch, and no fewer than 400 can be protein. The varied diet is to be made of two foods: A and B. Food A costs $0.75 per pound and contains 600 calories, 400 of which are protein and 200 starch. No more than two pounds of food A can be used per resident. Food B costs $0.15 per pound and contains 900 calories, of which 700 are starch, 100 are protein, and 100 are fat. (Answers in Appendix D) a. Write the equations representing this information. b. Solve the problem graphically for the amounts of each food that should be used.

Explanation / Answer

Let, A = pounds of Food A

B = pounds of food B

Here, the basic idea is to minimize the total calories based on the diet. Therefore, the equation would be -

Minimize : z = 0.75A + 015B

s.t 600A + 900B < 3600 Maximum calories

600A + 900B > 1800 Minimum calories

200A + 700B < 1400 Maximum starch

400A + 100B > 400 Minimum protein

A < 2 Minimum amount of A

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