Assignment:
Discuss the below:
1. Nick has plans to open some pizza restaurants, but he is not sure how many to open. He has prepared a payoff table to help analyze the situation.
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States of Nature
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Alternatives
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Good Market
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Fair Market
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Poor Market
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Open 1
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380,000
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70,000
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-400,000
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Open 2
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200,000
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80,000
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-200,000
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Do Nothing
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0
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0
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0
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Nick believes there is a 40 percent chance that the market will be good, a 30 percent chance that it will be fair, and a 30 percent chance that it will be poor. A market research firm will analyze market conditions and will provide a perfect forecast (they provide a money back guarantee). What is the most that should be paid for this forecast?
(a) $ 44,000
(b) $ 53,000
(c) $123,000
(d) $176,000
(e) none of the above
2. Daily sales for a perishable food product are known to be 8, 9, 10, or 11 cases with probabilities 0.2, 0.3, 0.4, and 0.1, respectively. Cases not sold during the day are worthless, but cases can only be produced in the morning before the store opens. The cost of producing one of these is $4 while the selling price is $7. If you choose to produce 10 cases in the morning to sell, what is the probability that you will be able to meet today's demand?
(a) 0.20
(b) 0.30
(c) 0.40
(d) 0.10
(e) 0.90
3. Daily sales for a perishable food product are known to be 8, 9, 10, or 11 cases with probabilities 0.2, 0.3, 0.4, and 0.1, respectively. Cases not sold during the day are worthless, but cases can only be produced in the morning before the store opens. The cost of producing one of these is $4 while the selling price is $7. How many cases should you produce to maximize profit?
(a) 8
(b) 9
(c) 10
(d) 11
(e) none of the above
4. Consider the following two-person game, and determine the saddle point if it exists.
Y1 Y2
X1 4 6
X2 2 3
(a) 3
(b) 2
(c) 4
(d) 6
(e) there is no saddle point
5. Considering the following two-person game, what percentage of the time should X play strategy X2?
Y1 Y2
X1 6 3
X2 2 8
(a) 1/3
(b) 2/3
(c) 4/9
(d) 5/9
(e) none of the above
Given the following two-person game, which strategy can be eliminated by use of dominance?
Y1 Y2
X1 13 9
X2 6 8
X3 12 14
(a) X1
(b) X2
(c) X3
(d) Y1
(e) Y2
6. Enrollment in a particular class for the last four semesters has been 120, 126, 110, and 130. Suppose a one-semester moving average was used to forecast enrollment (this is sometimes referred to as a naive forecast). Thus, the forecast for the second semester would be 120, for the third semester it would be 126, and for the last semester it would be 110. What would the MSE be for this situation?
(a) 196.00
(b) 230.67
(c) 100.00
(d) 42.00
(e) none of the above
7. Given the MAD for the following forecast is 4.0 what is the forecast value in period 4?
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Period
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Forecast
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Actual
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1
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15
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11
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2
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20
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13
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3
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25
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21
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4
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23
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(a) 24
(b) 30
(c) 23
(d) 33
(e) none of the above