The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and for each twin bed is $150. The manager's goal is to maximize profits. What is the weekly profit when ordering the optimal amounts?

The weekly profit when ordering the optimal amounts is $42,000

Step-by-step explanation:

Cost of one double bed = $500, storage space of one double bed = 100 cubic feet

Cost of one twin bed = $300, storage space of one twin bed = 90 cubic feet

Capital for the week = $75,000

Storage capacity of warehouse = 18,000 cubic feet

Profit for each double bed = $300

Profit for each twin bed = $150

Since the capital for the week is $75,000 and the storage capacity of the warehouse is 18,000 cubic feet, the optimal amounts the operations manager can order is 90 double bed and 100 twin bed

Cost of ordering 90 double bed = 90 * $500 = $45,000

Storage space = 90 * 100 cubic feet = 9000 cubic feet

Cost of ordering 100 twin bed = 100 * $300 = $30,000

Storage space = 100 * 90 cubic feet = 9,000 cubic feet

Total cost = $45,000 + $30,000 = $75,000

Total storage space = 9,000 cubic feet + 9,000 cubic feet = 18,000

Therefore, weekly profit = (90 * $300) + (100 * $150) = ($27,000 + $15,000) = $42,000