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A.2
Even though independent gasoline stations have been having a difficult time, Susan Helms has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susan developed the following table:
| Size of First Station | Good Market ($) | Fair Market ($) | Poor Market ($) |
| Small | 50000 | 20000 | -10000 |
| Medium | 80000 | 30000 | -20000 |
| Large | 100000 | 30000 | -40000 |
| Very Large | 300000 | 25000 | -160000 |
For example, if Susan constructs a small station and the market is good, she will realize a profit of $50,000.
e) Develop a decision tree. Assume each outcome is equally likely, then find the highest EMV.
• A.3
Clay Whybark, a soft-drink vendor at Hard Rock Cafe’s annual Rockfest, created a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd):
| States of Nature ( demand) | |||
| Alternatives | Big | Average | Small |
| Large Stock | $ 22000 | $ 12000 | -$ 2000 |
| Average Stock | $ 14000 | $ 10000 | $ 6000 |
| Small Stock | $ 9000 | $ 8000 | $ 4000 |
The probabilities associated with the states of nature are 0.3 for a big demand, 0.5 for an average demand, and 0.2 for a small demand.
a) Determine the alternative that provides Clay Whybark the greatest expected monetary value (EMV).
b) Compute the expected value of perfect information (EVPI).
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