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 theroom at least two weeks in advance (this helps to distinguish between leisure travelers whotend to book early, and business travelers who value the flexibility of booking late). 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:

# rooms demanded	Probability	Cumulative Probability	Range
10-25	5%	5%	15
26-41	10%	15%	15
42-57	20%	35%	15
58-73	30%	65%	15
74-89	20%	85%	15
90-105	10%	95%	15
106-121	5%	100%	15
Please note that any unsold room that was protected for business travelers will not bring any revenue, i.e., it will remain vacant.

d. 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.

c. 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]?

b. What does the optimal solution tell you about the expected marginal revenue from the business travelers? Please explain.

a. 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.)