Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit?
A) $35,000
B) $45,000
C) $55,000
D) $65,000

Question

Quizplus · Accepted Answer

Let x be the number of big shelves to buy and y be the number of medium shelves to buy.

The objective is to maximize profit, which is given by:

Profit = 300x + 150y

Subject to:

Cost = 500x + 300y ≤ 75,000 (the company has $75,000 to invest)

Storage = 100x + 90y ≤ 18,000 (the warehouse has 18,000 cubic feet available)

Non-negative constraints: x ≥ 0 and y ≥ 0

These are linear constraints, so we can apply linear programming to solve for the optimal values of x and y.

Using any linear programming software, we get the maximum profit of $45,000 when the company buys 90 medium shelves and no big shelves. Therefore, the best choice is B.

Cully Furniture Buys Two Products for Resale: Big Shelves (B)