Question

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?

Answer 1

Answer:

$45,000

Explanation:

Cully's storage constraint is: 100B + 90M ≤ 18000

If Cully were to buy only big shelves, it could buy 180 of them (= 18,000 / 100)

If they were to buy only medium shelves, it could buy 200 (= 18,000 / 90)

Cully's money restraint is: 500B + 300M ≤ 75,000

If Cully were to buy only big shelves, it could buy 150 of them (= 75,000 / 500)

If they were to buy only medium shelves, it could buy 250 (= 75,000 / 300)

So Cully's order must be within 150 big shelves and 200 medium shelves.

If Cully purchases and sells 150 big shelves, it will earn $45,000 in profit.

If Cully purchases and sells 200 medium shelves, it will earn $30,000 in profit.

Since the profit for big shelves is $500, Cully should try to sell as many of them as possible. The maximum amount that they can buy is 150, which will result in a $45,000 profit.