The Springer Dog Food Company makes dry dog food from two ingredients. The two ingredients (A and B) provide different amounts of protein and vitamins. Ingredient A provides 16 units of protein and 4 units of vitamins per pound. Ingredient B provides 8 units of protein and 8 units of vitamins per pound. Ingredients A and B cost $0.50 and $0.20 per pound, respectively. The company wants its dog food to contain at least 12 units of protein and 6 units of vitamins per pound and be as inexpensive as possible.
a. Reformulate an LP model for this problem.
b. Sketch the feasible region for this problem.
c. Determine the optimal solution to the problem by enumerating the corner points.
d. How will the optimal solution change if the company requires only 5 units of vitamins per pound rather than 6?