Question

A carpenter makes bookcases in two sizes, large(x) and small(y). It takes 6 hours to make a large bookcase and 2 hoursto make a small one. The profit on a large bookcase is $50 and the profit on a small bookcase is $20. The carpenter canspend no more than 24 hours per week making bookcases and must make at least two of each size each week. Howmany of each size must be made per week in order to maximize profit?

Answer 1

Step 1 : We have:

Large bookcases = 6x

Small bookcases = 2y

Hours per week = 24

Step 2: Let's write the inequality relating bookcases and hours, as follows

6x + 2y ≤ 24

Step 3: Let's write the inequality relating number of bookcases and time

2x + 2y