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QUESTION 2 Value of information Show all calculations to support your answers. You may follow the methods shown in the mp4 on Value of info for a way to answer this question if you wish. 20 marks - 4 for (a), 8 for (b), 2 for (c), 6 for (d) A manufacturer is trying to choose between two production methods (a1 and a2) for a new product. He considers that the probability of demand for the new product being good (s1) is 0.3 and the probability that demand will be poor (s2) is 0.7. In evaluating the two production methods the manufacturer has calculated the following table of conditional profits: s1 s2 a1 30,000 16,000 a2 10,000 24,000 a) Which production method should be used? Show calculations. The manufacturer asks a marketing consult for an opinion as to whether demand will be good or poor. From previous experience when the consultant has indicated that demand will be good she has been right 80% of the time, and when she has indicated that demand will be poor she has been right 65% of the time. b) Revise the prior probabilities in light of the consultant’s track record. c) What is the posterior probability of good demand given that the consultant has indicated demand will be good? d) What is the expected net gain or loss from engaging the consultant? Should the consultant be engaged? Explain the reasoning for your answer.