A competing hotel has 250 rooms with standard Queen-size beds and two rates: a full price of $250 and a discount price of $150. 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). You may assume that if a leisure traveler is not able to get the discount rate, she will choose to book at another hotel. For a particular Tuesday night, the hotel estimates that the average demand by business travelers has a mean of 80 rooms and a standard deviation of 35 rooms. Assume that demand follows a Normal distribution around the forecast. a) Find the optimal protection level for full price rooms (the number of rooms to be protected from sale at a discount price). b) Find the booking limit for discount rooms. c) Suppose that for a short time, the hotel's forecast of business customer demand is biased upward: the forecast of 80 rooms is too high and fewer business customers appear, on average. Qualitatively describe the economic consequences of using the protection level and booking limit derived in (a) and (b). d) Suppose that for a short time, the hotel's forecast of business customer demand is biased downward: the forecast of 80 rooms is too low and more business customers appear, on average. Qualitatively describe the economic consequences of using the protection level and booking limit derived in (a) and (b).