AA 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 S0.75 per pound and contains 600 calories, 400 of which are protein and 200 starches. No more than two pounds of food A can be used per resident. Food B costs S0.15 per pound and contains 900 calories, of which 700 are starch, 100 are protein, and 100 are fat.
Formulate a linear program that solves for the optimal diet plan with the least cost, and solve it using the graphical method. What's the optimal diet plan?