The AMC 24-plex cinema is trying to decide how many screens it should have showing the new action comedy movie Lost Wages in Las Vegas. The theater must sign a contract with the movie’s distributor...

The AMC 24-plex cinema is trying to decide how many screens it should have showing the new action comedy movie Lost Wages in Las Vegas. The theater must sign a contract with the movie’s distributor indicating how many screens it will play the movie on before reviews of the movie are public. The manager has decided, based on the actors involved in the movie, to devote between one and five screens to this movie during its two-week summer run. The profit the manager expects to earn on the movie is based on the consensus review of the movie (one to four stars). The payoff table showing these estimated profits is as follows.

a. If the theater manager wishes to minimize his maximum regret, how many screens should the movie be booked in?

b. If the theater manager is risk averse and wishes to use the maximin criterion, how many screens should the movie be booked in?

c. Suppose the theater manager believes, based on the director’s previous releases, that the probability the movie will be rated one star is .10, two stars .20, three stars .40, and four stars .30. If the manager wishes to use the expected value criterion, how many screens should the movie be booked in?