Chapter 5, Problem 16RE

In problems 15 and 16, 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 by the indicated method.

Animal food. A special diet for laboratory animals is to contain at least $850$ units of vitamins, $800$ units of minerals, and $1,150$ calories. There are two feed mixes available, mix $A$ and mix $B$. A gram of mix $A$ contains $2$ units of vitamins, $2$ units of minerals, and $4$ calories. A gram of mix $B$ contains $5$ units of vitamins, $4$ units of minerals, and $5$ calories.

(A) If mix $A$ costs $\text{\$}0.04$ per gram and mix $B$ costs $\text{\$}0.09$ per gram, how many grams of each mix should be used to satisfy the requirements of the diet at minimal cost? What is the minimum cost?

(B) If the price of mix $B$ decreases to $\text{\$}0.06$ per gram, discuss the effect of this change on the solution in part (A).

(C) If the price of mix $B$ increases to $\text{\$}0.12$ per gram, discuss the effect of this change on the solution in part (A).