Chapter 12.1, Problem 16E

City Electronics Distributors handles two lines of televisions, the Packard and the Bell. It purchases up to $\$57000$ worth of television sets from the manufacturers each month and stores them in a $9,000$-cubic-foot warehouse. The Packards come in $36$-cubic-foot packing crates, and the Bells come in $30$-cubic-foot crates. The Packards cost City Electronics $\$200$ each and can be sold to a retailer for a $\$200$ profit, while the Bells cost $\$250$ each and can be sold for a $\$260$ profit. City Electronics must stock enough sets to meet its regular customers’ standing orders.

a. If City Electronics has standing orders for $250$ sets in addition to orders from other retailers, how many sets should City Electronics order each month to maximize profit?

b. If City Electronics’ standing orders increase to $260$ sets, how many sets should City Electronics order each month to maximize profit?