Kentwood Electronics manufactures three components for stereo systems: CD player

Question

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 CostCD Player $150 $75Tape Deck $85 $35Stereo Tuner $70 $30Each 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 Kentwood 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?I have quite a bit of this done, but I don't see where I can put an attachment up. Please let me know if you can help.Thank you

Explanation / Answer

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 price-Manufacturing cost                       

Profit per CD player= $150-75=$75

Profit per tape deck=$85-35=$50

Profit per stereo tuner=$70-30=$40

  Thus, Objective function would be:

Z=MAX (75*150) X1 + (50*150) X2 + (40*150) X3

ST (3*150) X1 + (2*150) X2 + (1*150) X3 400,000 (Assembly time constraint)

X1<=150,000/150 (Maximum Batches of CDs)

X1>=50,000/150 (Minimum Batches of CDs)

X2<=100,000/150 (Maximum Batches of Tape Decks)

X2>=50,000/150 (Minimum Batches of Tape Decks)

X3<=90,000/150 (Maximum Batches of Stereo Tuners)

X3>=50,000/150 (Minimum Batches of Stereo Tuners)

X1, X2, X3>=0 and Integer

a.       Create a spreadsheet model for this problem and solve it.

See the attached excel file:187113_Solution.xls

b.      What is the optimal solution?       

CD Players=466, Tape decks=334, Stereio tuners=600

                Maximum profit = $11,347,500

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