Chapter 8, Problem 37T

A weight lifter wants to mix two types of protein powder. One is a whey protein and one is a soy protein. The fat carbohydrate, and protein content (in grams) for $1$ scoop of each powder is given in the table.

Suppose that the weight lifter wants to make at most $60$ scoops of a protein powder mixture. Furthermore, he wants to limit the total fat content to at most $150\text{ g}$ and the total carbohydrate content to at most $216\text{ g}\text{.}$

a. Determine the number of scoops of each type of powder that will maximize the total protein content under these constraints.

b. What is the maximum total protein content?

c. If the protein content were reversed between the two brands (that is, $18\text{ g}$ for the whey protein and $20\text{ g}$ for the soy protein), then how much of each type of protein powder should be used to maximize the amount of protein?