The Hyatt hotel has 150 rooms with standard king beds and two rates: a full price of $200 per night and a discount price of $120 per night. To receive the discount price, a customer must purchase the room at least two weeks in advance. For a particular night, the hotel estimates that the demand from leisure travelers (who book at the discounted price) could fill the whole hotel while the demand from the business travelers (who book at the full price) is distributed normally with a mean of 70 rooms and a SD of 29 rooms. a. Find the optimal protection level (i.e., the number of rooms to be protected for business travelers) for full-price rooms. b. The Sheraton hotel nearby declared a fare war by slashing business travelers price down to $150. The Hyatt had to match that price to keep the demand at the same level. How does the optimal protection level change? c. What numbers of rooms on average remain unfilled if Hyatt establishes a protection level of 61 rooms? d. If Hyatt were able to ensure that every full-price customer would receive a room, what would its expected revenue be? e. If Hyatt did not protect any rooms for the full-price customers and if leisure travelers booked before the business travelers, then what would the expected revenue be? f. Taking the assumptions in part (e) above, and assuming that Hyatt protects 50 rooms for the full price, what is its expected revenue