The Inn at Penn hotel has 150 rooms with standard queen-size beds and two rates: a full price of $200 and a discount price of $120. To receive the discount price, a customer must purchase the room at least two weeks in advance (this helps to distinguish between leisure travelers, who tend to book early, and business travelers, who value the flexibility of booking late). For a particular Tuesday night, the hotel estimates that the demand from leisure travelers could fill the whole hotel while the demand from business travelers is distributed normally with a mean of 70 rooms and a standard deviation of 29.
a. Suppose 50 rooms are protected for full-price rooms. What is the booking limit for the discount rooms?
b. Find the optimal protection level for full-price rooms (the number of rooms to be protected from sale at a discount price).
c. The Sheraton declared a fare war by slashing business travelers' prices down to $150. The Inn at Penn had to match that fare to keep demand at the same level. Does the optimal protection level increase, decrease, or remain the same? Explain your answer.
d. What number of rooms (on average) remain unfilled if we establish a protection level of 61 for the full-priced rooms?
e. If The Inn were able to ensure that every full-price customer would receive a room, what would The Inn's expected revenue be?
f. If The Inn did not choose to protect any rooms for the full price and leisure travelers book before business travelers, then what would The Inn's expected revenue be?
g. Taking the assumptions in part f and assuming now that The Inn protects 50 rooms for the full price, what is The Inn's expected revenue?