An entrepreneur wants to determine whether it would be profitable to establish a gardening service in a local suburb. The entrepreneur believes that there are four possible levels of demand for this gardening service: Very low demand—1% of the households would use the service. Low demand—5% of the households would use the service. Moderate demand—10% of the households would use the service. High demand—25% of the households would use the service. Based on past experiences in other suburbs, the entrepreneur assigns the following probabilities to the various demand levels: P(High demand) = 0.10 P(Moderate demand) = 0.20 P(Low demand) = 0.50 P(Very low demand) = 0.20 The entrepreneur has calculated the following profits or
losses ($) of this garden service for each demand level (over a period of one year): ACTION DEMAND Provide Garden Service Do Not Provide Garden Service Very low -50,000 0 Low 60,000 0 Moderate 130,000 0 High 300,000 0 a. Construct a decision tree. b. Construct an opportunity loss table. c. Compute the expected monetary value (EMV) for offer- ing this garden service. d. Compute the expected opportunity loss (EOL) for offer- ing this garden service. e. Explain the meaning of the expected value of perfect information (EVPI) in this problem. f. Compute the return-to-risk ratio (RTRR) for offering this garden service. g. Based on the results of (c), (d), and (f ), should the entre- preneur offer this garden service? Why? Before making a final decision, the entrepreneur conducts a survey to determine demand for the gardening service. A random sample of 20 households is selected, and 3 indicate that they would use this gardening service. h. Revise the prior probabilities in light of this sample infor- mation. (Hint: Use the binomial distribution to determine the probability of the outcome that occurred, given a par- ticular level of demand.) i. Use the revised probabilities in (h) to repeat (c) through (g).