QUESTION 4: Decision Analysis(14 points)

The Sunshine Health Club is considering an expansion. Two proposals are being considered. Each one has been analyzed in terms of its revenue generating potential under three levels of customer response, and the information is shown below.

Customer Response

ProposalHighModerateLow

Add aquatic center150,00050,000-80,000

Double current capacity100,00040,000-20,000

No change70,00030,000 10,000

Sunshine's general Manager, Joy Smiley, estimates the probabilities of the customer response levels (High, Moderate, and Low) to be 0.45, 0.3 and 0.25 respectively.

(a)Using the Expected Payoff (i.e. EP or EMV) criterion, what proposal should Sunshine health club choose? (3 points)

(b)Suppose that Joy has a fantastic option to buy PERFECT information regarding the customer response. Such information will allow her to make a decision under certainty. Joy has to pay $10,000 for this perfect information. Should she pay? Show your work. (4 points)

Joy can order a survey service conducted by a fitness trade association. The survey will indicate either a positive or negative growth. Joy is given first the following conditional probability information regarding the quality of the survey.

P(positive indicator | high response) = 0.92

P(positive indicator | moderate response) = 0.56

P(positive indicator | low response) = 0.10

Joy's prior belief about the probability of each possible level of response follows her initial estimation, i.e. 0.45, 0.3 and 0.25 for high, moderate, and low response respectively.

(c)If Joy decides to use the survey, what would the revised probabilities (posterior probabilities) be for the customer response, and what would the probabilities be for the positive and negative survey results? Show your work. (7 points)