The Inn at Penn 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 lease two weeks in advance ( this helps to distinguish between the business travelers, who value the flexibility of booking late and leisure travelers who tend to book early). For a particular Wednesday night, the hotel estimates that the demand from the leisure travelers could fill the whole hotel while the demand from business travelers follows the following empirical distribution

Number of rooms demanded Probability

10-25 0.05

26-41 0.10

42-57 0.20

58-73 0.30

74-89 0.20

90-105 0.10

106-121 0.05

Please note that any unsold room that was protected for business travelers will not bring any revenue, i.e., it will remain vacant.

1. Find the optimal number of rooms to be kept for business travelers (i.e., number of rooms to be protected from sale at a discount.)
2. What does the optimal solution tell you about the expected marginal revenue from the business travelers? Please explain.
3. What would be the optimal number of rooms kept for business travelers if the number of rooms demanded by the business travelers was uniformly distributed on [10,120]?
4. The Sherhilton Hotel 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. What will be the optimal protection level using the uniform distribution given in part (c) above. Please explain your answer.