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. martin has analyzed the situation and 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 ahve been determined.
Decision Alternatives Heavy, s1 Moderate, s2 Light, s3
Blade Attachment, d1 3500 1000 -1500
New Snowplow, d2 7000 2000 -9000
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)= .80 P(s1l N) =.35 P(s1 l U) = .62
P(U) = .20 P(s2 l N) = .30 P(s2 l U) = .31
P(s3 l N)= .35 P(s3 l U)= .07
A. Construct a decision tree for this problem
B. what is the recommended decision if Martin does not wait until September? What is the 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 the September weather is determined? What is the expected value of this decision strategy?