Chapter 20.3, Problem 12E

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

1. a. Construct a decision tree for this problem.
2. b. W hat is the recommended decision if Martin does not wait until September? What is the expected value?
3. c. W hat is the expected value of perfect information?
4. 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?