Chapter 12.1, Problem 15E

The Appliance Barn has $2,400$ cubic feet of storage space for refrigerators. The larger refrigerators come in $60$-cubic-foot packing crates, and the smaller ones come in 40-cubic-foot crates. The larger refrigerators can be sold for a $\$250$ profit, while the smaller ones can be sold for a $\$250$ profit.

a. If the manager is required to sell at least $50$ refrigerators each month, how many large refrigerators and how many small refrigerators should he order each month to maximize profit?

b. If the manager is required to sell at least $40$ refrigerators each month, how many large refrigerators and how many small refrigerators should he order each month to maximize profit?

c. Should the Appliance Barn owner require his manager to sell $40$ or $50$ refrigerators per month?