Question 1 (8 points): Your friend is still the owner of Sweetilicious, a local cupcake shop in Geneseo, NY. Recently, Letchworth Bakery, a local competitor of Sweetilicious, gave your friend an offer again to sell the shop for $100,000. Suppose that the probabilities of Sweetilicious' expected profits in the future are given as follows: P($80,000) = 0.2, P($100,000) = 0.3, P($120,000) = 0.1, and P($140,000) = 0.4. a. Do you recommend your friend to sell the shop? Apply expected value approach. Hint: Since there are four different scenarios for the future profitability, you can consider there are three different states of nature. b. Now, your friend considers hiring Letchworth Advisor, another local research & consulting firm, to get some information on future local business conditions. The forecast information may indicate either O (which means good condition) or X (which means bad condition). Suppose that conditional probabilities of the forecast indicators that are conditional on Sweetilicious' expected profitability are given as follows: P(O| $80,000) = 0.1; P(O | $100,000) = 0.2; P(O | $120,000) = 0.6; P(O | $140,000) = 0.3 If the consulting service costs $10,000, do you recommend your friend to hire Letchworth Advisor? Why or why not? Include a decision tree in your answer to visualize this decision-making problem. Hint: Explain your answer by computing EVSI (expected value of sample information). You may also need to compute branch probabilities. The use of a tabular approach will help you. c. What is Expected Value of Perfect Information, EVPI? Recall that EVPI = |EV w/ PI - EV w/o PI|. d. As studied in class, using a graph, provide the Risk Profile for the case of X, bad local business condition. Be sure to label probabilities and expected values.