Question four A contractor is invited to bid on a construction job. The value of the contract depends on the time taken to finish the project. If the project is finished on time, there is a profit of $1,000,000, but if it is finished late, there is a loss of $200,000. Weather is the sole determinant if the project is finished on time or late. If the weather is good, the contractor will be done on time but if the weather is bad, the project will be late. Currently, there is a prior probability of 20% that the weather will be good (Good weather = on time; bad weather = late). The contractor must decide whether or not to bid. The contractor has the opportunity to buy a long-range weather forecast from a private weatherforecasting company which has a fairly good track record with these forecasts. Records show that 70% percent of the time it successfully predicted good weather (favourable) and 80% of the time it successfully predicted bad weather (unfavourable). That is, in the past when there was actually good weather it said favourable 70% beforehand and said unfavourable 30% of the time beforehand. Also, in the past when there was actually bad weather it said unfavourable 80% beforehand and said favourable 20% of the time beforehand. The company charges $50,000 for the forecast. The following table summarises the payoffs. States of Nature with Profits ($) Does not include forecast cost Decision Alternatives Good weather(G) Bad weather (B) Bid $1,000,000 ($200,000) No bid $0 $0 Prior Probabilities P(G) = 0.20 P(B) = .80 Conditional probability for a given state of nature where forecasts are either favourable (F) or unfavourable (U):That is: P(F|G) = 0.70; P(U|G) = 0.30; P(F|B) = 0.20; P(U|B) = 0.80 After you have computed the revised probabilities, round to two decimal places. After you have computed the revised probabilities, round to two decimal places. (a) Construct the appropriate decision tree to help the contractor choose the best option. This tree must be constructed in logical order (5 marks). This includes the revised probabilities (5 marks) as well as labels and net payoffs. (10 marks) (b) Fold back the decision tree (4 marks) to determine the best strategy for the contractor - he wants to maximize profit. (You must state this strategy: 2 marks). What is the final expected profit? (1 mark) total (7 marks) (c) What is the expected value of sample information (EVSI) - the most that should be paid for the evaluation? (1 mark) (d) Calculate the expected value of perfect information (EVPI) - the most that should be paid to an expert for perfect prediction of the uncertain outcomes. (1 mark) (e) What is the efficiency of sample information? (1 mark)