Chapter 8, Problem 58RE

A fitness instructor wants to mix two brands of protein powder to form a blend that limits the amount of fat and carbohydrate but maximizes the amount of fiber. The nutritional information is given in the table for a single scoop of protein powder.

Suppose that the fitness instructor wants to make at most $180$ scoops of the mixture. She also wants to limit the amount of fat to $480\text{ g}$ and she wants to limit the amount of carbohydrate to $696\text{ g}\text{.}$

a. Determine the number of scoops of each type of powder that will maximum the amount of fiber.

b. What is the maximum amount of fiber?

c. If the fiber content were reversed between the two brands (that is, $8\text{ g}$ for brand $\text{A}$ and $10\text{ g}$ for brand $\text{B}$ ), then how much of each type of protein powder should be used to maximize the amount of fiber?