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The Bargain Hut has 2400 cubic feet of storage space for refrigerators. Large refrigerators come in 60-cubic-foot packing crates and small refrigerators come in 40-cubic-foot crates. Large refrigeratorscan be sold for a $250 profit and the smaller ones can be sold for $150 profit. How many of each typeof refrigerator should be sold to maximize profit and what is the maximum profit if:a) If the manager wants to sell at least 50 refrigerators must be sold each month, how many large refrigerators and how many smaller refrigerators should he/she order each month to maximize profit?b) At least 40 refrigerators must be sold each month.

Question

The Bargain Hut has 2400 cubic feet of storage space for refrigerators. Large refrigerators come in 60-cubic-foot packing crates and small refrigerators come in 40-cubic-foot crates. Large refrigerators
can be sold for a $250 profit and the smaller ones can be sold for $150 profit. How many of each type
of refrigerator should be sold to maximize profit and what is the maximum profit if:
a) If the manager wants to sell at least 50 refrigerators must be sold each month, how many large refrigerators and how many smaller refrigerators should he/she order each month to maximize profit?
b) At least 40 refrigerators must be sold each month.

check_circleAnswer
Step 1

First we develop the model for the problem which is an LP (Linear Programming) problem. Assuming L large refrigerators are sold and S small refrigerators are sold, then the model for part a) is given by:

 

Maximize Z = 250L + 150S  (profit)

Subject to the following constraints:

Space constraint: 60L + 40S <= 2400

Minimum sales requirement: L + S >= 50

 

Solving the model using LP solver (such as MS-Excel ®) we get the following results:

Maximum profit = $9500

Number of large refrigerator = 20

Number of smaller refrigerator = 30

Step 2

The model for part b) is very similar to that of part a) with only the second minimum sales constraint RHS changing to 40, so the new model is:

Maximize Z = 250L + 150S  (profit)

Subject to the following constraints:

Space constraint: 60L + 40S <= 2400

Minimum sales requirement: L + S >= 40

Solving the m...

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