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# Integer programming problem: Kentwood electronics

Kentwood Electronics manufactures three components for stereo systems: CD players, tape decks, and stereo tuners. The wholesale price and manufacturing cost of each item are:

Component Wholesale Price Manufacturing Cost
CD Player \$150 \$75
Tape Deck \$85 \$35
Stereo Tuner \$70 \$30

Each CD player produced requires three hours of assembly; each tape deck requires two hours of assembly; and each tuner requires one hour of assembly. However, the company manufactures these products only in batches of 150?partial batches are not allowed. The marketing department believes that it can sell no more than 150,000 CD Players, 100,000 tape decks, and 90,000 stereo tuners. It expects a demand for at least 50,000 units of each item and wants to be able to meet this demand. If Kenwood has 400,000 hours of assembly time available, how many batches of CD players, tape decks, and stereo tuners should it produce to maximize profits while meeting the minimum demand figures supplied by marketing?
a. Formulate an ILP model for this problem. (Hint: Let your decision variables represent the number of batches of each item to produce.)
b. Create a spreadsheet model for this problem and solve it.
c. What is the optimal solution?

#### Solution Preview

See attachments

X1 = batches of CD players to produce
X2 = batches of tape decks to produce
X3 = batches of stereo tuners to produce
As it is a profit maximization problem, Profit for a batch of each of the item needs to be calculated:
Profit= Wholesale ...

#### Solution Summary

This posting contains solution to following ILP problem using Excel solver.

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