Operational 12

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SPECIMEN DECISION ANALYSIS EXAMINATION 2

Time allowed: 2 hours Answer any THREE questions from the five questions supplied.

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Question 1 The Academy of Forecasting has to decide on a location for its annual symposium. Two locations are being considered: the Heraton hotel in New York and the campus of Atlantic University. The profit that the academy will earn from the symposium depends on the cost of the location and the number of delegates attending. The cost to the Academy of holding the symposium at the Heraton will be a fixed charge of $14 000 plus and extra $100 per delegate. The Atlantic University will charge $10 000 plus an extra $120 per delegate. Delegates will pay $300 to attend the symposium, irrespective of which location is chosen. The number of delegates attending the symposium is likely to depend on the location. For simplicity, subjective probability distributions for the number of delegates attending at each location have been approximated by the three-point distributions shown below. Heraton Hotel No. of delegates attending 50 100 150 Probability 0.2 0.5 0.3 Atlantic University No. of delegates attending 40 100 160 Probability 0.4 0.5 0.1

a) Identify the location that will maximize the expected profit earned by the Academy. (25% of marks on question) b) What reservations do you think the Academy should have about using your analysis in part (a) to choose the location for the symposium? (25% of marks on question) c) After a utility elicitation session, the Academy's treasurer is able to make the following statements: ‘I would be indifferent between earning a profit of $15 200 for certain and taking a gamble which had a 0.99 probability of yielding a profit of $16 000 and a 0.01 probability of yielding a loss of $4000.’ ‘I would be indifferent between earning a profit of $8000 for certain and taking a gamble which had a 0.92 probability of yielding a profit of $16 000 and a 0.08 probability of yielding a loss of $4000.’ ‘I would be...