Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelv

Question

Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased?

Explanation / Answer

In the question the space available is 18000 cubic feet for storage. If the space is used by all the Big shelves then 180 shelves can be stored and profit is 180*85 = 15300. And similarly if all the space is used by Mediun Shelves, then it can store 18000/80 = 225 Medium Shelves and so Profit = 225*75 = 16875.

So in order to maximize the profit 225 Medium Shelves should be purchased.

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