Even though independent gasoline stations have been having a difficult time, Susan Solomon 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 ($)
For example, if Susan constructs a small station and the market is good, she will realize a profit of $50,000.
a. Develop a decision table for this decision.
b. What is the maximax decision?
c. What is the maximin decision?
d. What is the equally likely decision?
e. What is the criterion of realism decision? Use an α value of 0.8.
f. Develop an opportunity loss table.
g. What is the minimax regret decision?
3-40 Bill Holliday is not sure what he should do. He can build a quadplex (i.e., a building with four apartments), build a duplex, gather additional information, or simply do nothing. If he gathers additional information, the results could be either favorable or unfavorable, but it would cost him $3,000 to gather the information. Bill believes that there is a 50–50 chance that the information will be favorable. If the rental market is favorable, Bill will earn $15,000 with the quadplex or $5,000 with the duplex. Bill doesn’t have the financial resources to do both. With an unfavorable rental market, however, Bill could lose $20,000 with the quadplex or $10,000 with the duplex. Without gathering additional information, Bill estimates that the probability of a favorable rental market is 0.7. A favorable report from the study would increase the probability of a favorable rental market to 0.9. Furthermore, an unfavorable report from the additional information would decrease the probability of a favorable rental market to 0.4. Of course, Bill could forget all of these numbers and do nothing. What is your advice to Bill?
