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# Inn at Penn has 100 rooms.

Inn at Penn has 100 rooms. For regular-fare customers, rooms are priced at $ 225 per night while the rooms are priced at $650 per night for the high-paying customers who generally arrive at the last minute. The demand for such high fare customers is normally distributed with a mean of 40 and standard deviation of 6. Assume that there is ample demand for regular-fare customers.

a. What should the protection level for the high fare be to maximize expected profit?

b. Suppose that Inn at Penn operates with the protection level of 50 rooms for high fare customers. On average, how many high-fare customers are turned away because of lack of rooms?

c. Suppose again that the Inn at Penn operates with the protection level of 45 rooms for high fare customers. What is the probability that there are at least 3 rooms left unoccupied?