A college has sold out all tickets for a jazz concert to be held in the stadium.

Question

A college has sold out all tickets for a jazz concert to be held in the stadium. If it rains, the show will have to be moved to the gym, which has a much smaller capacity. The dean must decide in advance whether to set up the seats and the stage in the gym or in the stadium, or both, just in case. The payoff matrix below shows the net profit in each case. Complete parts a through c below. States of Nature Rain No Rain $1550 S1500 $1000 S1000 $750 S1400 Set Up in Stadium StrategiesSet Up in Gym (a) What strategy should the dean choose if she is an optimist? If the dean is an optimist, she should set up in the stadium. (b) What strategy should the dean choose if she is a pessimist? If the dean is a pessimist. she should set up in the gym. (c If the weather forecaster predicts rain with a probabi ity of 06, what strategy should the dean choose to maximize expected profit? If the probability of rain is 0.6, the dean shouid set up in both to maximize expected profit. What is the maximum expected profit? s(Simplify your answer.) Set Up in Both

Explanation / Answer

(a) If the dean is an optimist, he doesn't expect rain. So in order to optimize profit the concert should be in the stadium.

(b) If the dean is a pessimist, he expects a rain. So, in order to optimize profit, the concert should be in the gym.

(c) If the weather forecast is rain with a probablity of 0.6, then

Profit if it is scheduled in stadium, -1550*0.6 + 1500*0.4 = -330

Profit if it is scheduled in the gym , 1000*0.6 + 1000*0.4 =

1000

Profit if it is scheduled in both, 0.6*750+ 0.4*1400=1010

Hence, it should be scheduled in both.

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