Inn at Penn has 200 rooms. For regular-fare customers, rooms are priced at $300 per night while the rooms are priced at $700 per night for the high-paying customers who generally arrive at the last minute. The demand for such high fare customers is distributed normally with mean 60 and standard deviation 50. 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 80 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 80 rooms for high fare customers. What is the probability that there are at least 5 rooms left unoccupied?