Question

You are in charge of purchases at the student-run used-book supply program at your college, and you must decide how many introductory calculus, history, and marketing texts should be purchased from students for resale. Due to budget limitations, you cannot purchase more than 850 of these textbooks each semester. There are also shelf-space limitations: Calculus texts occupy 2 units of shelf space each, history books 1 unit each, and marketing texts 5 units each, and you can spare at most 1,500 units of shelf space for the texts. If the used book program makes a profit of $20 on each calculus text, $8 on each history text, and $16 on each marketing text, how many of each type of text should you purchase to maximize profit?

Answer 1

you should purchase 750 calculus books that will yield $15,000 in profits.

Step-by-step explanation:

you have to maximize the following equation 20C + 8H + 16M

where:

C = calculus book

H = history book

M = marketing book

the constraints are

C + H + M ≤ 850 (total number of books)

2C + H + 5M ≤ 1500 (maximum amount of shelf-space)

using Solver, the optimal solution is 750 calculus books