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.

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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