Question

A school drama club budgets $1,500 to purchase costumes. They must purchase a minimum of 150 costume pieces to meet the show's needs. If they purchase basic props for $3.50 each and premium costumes for $15.00 each, what is the maximum number of premium costumes the club can purchase to stay within the budget and meet the minimum quantity requirement?

Answer 1

Let p = number of premium costumes and b = number of basic props. Constraints:
- p + b ≥ 150
- 15p + 3.5b ≤ 1500

To maximize p, take the minimum b = 150 − p. Substitute:
15p + 3.5(150 − p) ≤ 1500
15p + 525 − 3.5p ≤ 1500
11.5p ≤ 975
p ≤ 975/11.5 ≈ 84.78

So the maximum integer number of premium costumes is 84. (Check: 84 premiums and 66 basics cost 84·15 + 66·3.5 = $1,491 ≤ $1,500; 85 premiums would exceed the budget.)