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 prot 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 xed 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 Atlantic University No. of delegates attending Probability No. of delegates attending Probability 50 0.2 40 0.4 100 0.5 100 0.5 150 0.3 160 0.1 a) Identify the location that will maximize the expected prot 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) 0) After a utility elicitation session, the Academy's treasurer is able to make the following statements: '1 would be indifferent between earning a prot of $15 200 for certain and taking a gamble which had a 0.99 probability of yielding a prot of $16 000 and a 0.01 probability of yielding a loss of $4000.' '1 would be indifferent between earning a prot of $8000 for certain and taking a gamble which had a 0.92 probability of yielding a prot of $16 000 and a 0.08 probability of yielding a loss of $4000.' '1 would be indifferent between earning a prot of $6000 for certain and taking a gamble