The Inn at Penn hotel has 150 rooms with standard queen-size beds and two rates: a full price of $300 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 with a normal distribution with a mean 1000 and a standard deviation of 100. Historically, the hotel estimates that the demand from business travelers is distributed normally with a mean of 70 rooms and a standard deviation of 29. a. The optimal booking limit for discount rooms is . (Hint: please round your answer to the nearest positive integer number. E. g., answers between 12345.01 and 12345.44 should be rounded down to 12345, and answers between 12345.45 and 12345.99 should be rounded up to 12346.) .
b. The Sheraton located nearby declared a fare war by slashing business travelers’ price to $150. The Inn at Penn had to match that fare to keep demand at the same level, so the optimal booking limit will . (Hint: please fill in the blank by one of the following three options:
increase, decrease, or remain the same)
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?