IS 603 Assignment #1: Decision Modeling
1. An auto company manufactures cars and trucks. Each vehicle must be processed in the paint shop and body assembly shop.
If the paint shop were only painting trucks, 40 trucks could be painted per day. If the paint shop were only painting cars, 50 cars could be painted per day.
If the body shop were only assembling trucks, it could process 60 per day. If the body shop were only assembling cars, it could process 70 per day;
Additionally, auto dealers require that the auto company produces at least 5 trucks per day; but the number of produced trucks per day can’t exceed the number of produced cars by more than 25.
Each truck contributes $300 to profit, and each car contributes $200 to profit.
The decision problem for the auto company is to determine a daily production plan that will maximize the company’s profits.
Question: Can you create a linear programming model to determine how many cars and trucks should be produced on a weekly basis in order to achieve a maximum profit (You do NOT need to solve the model)?
2. Solve the following LP problem graphically using level curves (The graphical approach we discussed in the class):
max p = 12X1 + 8X2
subject to: 6X1 + 3X2 <= 24
2X1 + 4X2 <= 16
8X1 + 8X2 <= 40
X1, X2 >= 0
3. Mr. Green, the manager of the new products division of a tire manufacturer, has a decision-making problem under risk. He must choose one of the three alternative designs of a fairly expensive new non-skid tread to be put on the market. He figures out the following situations: if he recommends that the design A be put on the market, it may have 65% of chance to gain public acceptance, which will contribute $200,000 to his company; On the other hand, if he recommends the design A and it does not gain public acceptance, the resulting loss will be $120,000; if he recommends that the design B be put on the market, it may have 70% of chance to gain public acceptance, which will contribute $160,000 to his company; On the other hand, if he recommends the design B and it does not gain public acceptance, the resulting loss will be $100,000; Finally, if he recommends that the design C be put on the market, it may have 60% of chance to gain public acceptance, which will contribute $240,000 to his company; On the other hand, if he recommends the design C and it does not gain public acceptance, the resulting loss will be $160,000.
The question is: which design, A or B or C, should he recommend to be put on the market? Why? Please provide the detailed steps.
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