Chapter 6.4, Problem 35E

In Problems 33-38, construct a mathematical model in the form of a linear programming problem. (The answers in the back of the book for these application problems include the model). Then solve the problem using the big $M$ method.

Human nutrition. A person on a high-protein, low-carbohydrate diet requires at least $100$ units of protein and at most $24$ units of carbohydrates daily. The diet will consist entirely of three special liquid diet foods: $A,B,$ and $C$. The contents and costs of the diet foods are given in the table. How many bottles of each brand of diet food should be consumed daily in order to meet the protein and carbohydrate requirements at minimal cost? What is the minimum cost?