# Question

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:

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?

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:

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?

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