Problem 1: A diet is being prepared for the University of Arizona dorms. The objective is to feed the students at the least cost, but the diest must have between 1800 and 3600 calories. No more than 1400 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 starch, 100 are protein, and 100 are fat.
a. Write the equations representing this information.
b. Solve the problem graphically for the amounts of each food that should be used.
Problem 2: Repeat problem above with the added constraint that not more than 150 calories shall be fat and that the price of food has escalated to $1.75 per pound for food A and 2.50 round food B.