Chapter 5.3, Problem 52E

In Problems 49-64, 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 by the geometric method.

Animal food. A laboratory technician in a medical research center is asked to formulate a diet from two commercially packaged foods, food $A$ and food $B$, for a group of animals. Each ounce of food $A$ contains $8$ units of fat, $16$ units of carbohydrate, and $2$ units of protein. Each ounce of food $B$ contains $4$ units of fat, $32$ units of carbohydrate, and $8$ units of protein. The minimum daily requirements are $176$ units of fat, $1,024$ units of carbohydrate, and $384$ units of protein. If food $A$ costs $5\cancel{\text{c}}$ per ounce and food $B$ costs $5\cancel{\text{c}}$ per ounce, how many ounces of each food should be used to meet the minimum daily requirements at the least cost? What is the cost for this amount of food?