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?
A) $0
B) $30,000
C) $42,000
D) $45,000
E) $54,000

Question

Quizplus · Accepted Answer

To maximize profits, the manager should purchase as many double beds (D) as possible since they offer a higher profit margin ($300) compared to twin beds ($150). However, constraints are given by the budget ($75,000) and storage space (18,000 cubic feet).Let's calculate the maximum number of double beds that can be purchased within these constraints:1. Budget constraint for double beds: $75,000 / $500 = 150 beds.2. Storage constraint for double beds: 18,000 cubic feet / 100 cubic feet = 180 beds.The budget allows for the purchase of up to 150 double beds, and the storage space allows for up to 180 double beds. Therefore, the limiting factor is the budget, allowing for the purchase of 150 double beds.Profit from double beds = 150 beds * $300/bed = $45,000.Since purchasing 150 double beds does not exceed the budget or storage space, and it yields the highest possible profit given the constraints, $45,000 is the maximum weekly profit.

The Operations Manager of a Mail Order House Purchases Double