Martin’s Service Station is considering entering the snowplowing business for the coming winter season. Martin can purchase either a snowplow blade attachment for the station’s pick-up truck or a new heavy-duty snowplow truck. After analyzing the situation, Martin believes that either alternative would be a profitable investment if the snowfall is heavy. Smaller profits would result if the snowfall is moderate, and losses would result if the snowfall is light. The following profits/losses apply.
The probabilities for the states of nature are P(s1) = .4, P(s2) = .3, and P(s3) = .3. Suppose that Martin decides to wait until September before making a final decision. Assessments of the probabilities associated with a normal (N) or unseasonably cold (U) September are as follows:
P(N) = .8 | P(s1 | N ) 5 .35 | P(s1 | U ) 5 .62 |
P(U) = .2 | P(s2 | N ) 5 .30 | P(s2 | U ) 5 .31 |
P(s3 | N ) 5 .35 | P(s3 | U ) 5 .07 |
- a. Construct a decision tree for this problem.
- b. W hat is the recommended decision if Martin does not wait until September? What is the
expected value ? - c. W hat is the expected value of perfect information?
- d. W hat is Martin’s optimal decision strategy if the decision is not made until the September weather is determined? What is the expected value of this decision strategy?
Want to see the full answer?
Check out a sample textbook solutionChapter 20 Solutions
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill