Martin's Service Station is considering entering the snowplowing business for the comingwinter season. Martin can purchase either a snowplow blade attachment for the station'spick-up truck or a new heavy-duty snowplow truck. After analyzing the situation, Martinbelieves 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 thesnowfall is light.
The following profits/losses apply.State of NatureDecision Alternatives Heavy, s1 Moderate, s2 Light, s3Blade attachment, d1 3500 1000 1500New snowplow, d2 7000 2000 9000The probabilities for the states of nature are P(s1) .4, P(s2) .3, and P(s3) .3. Supposethat Martin decides to wait until September before making a final decision. Assessmentsof the probabilities associated with a normal (N) or unseasonably cold (U)September are as follows:P(N ) = .8P(U)= .2P(s1 / N ) = .35P(s2 / N )= .30P(s3 / N )= .35P(s1 / U )= .62P(s2 /U )= .31P(s3 /U ) = .07a. Construct a decision tree for this problem.
b. What is the recommended decision if Martin does not wait until September? What isthe expected value?
c. What is the expected value of perfect information?
d. What is Martin's optimal decision strategy if the decision is not made until theSeptember weather is determined? What is the expected value of this decision strategy?