Recall the yield management problem faced by the Eastman Towers Hotel, as described in the note "Introduction to the Theory and Practice of Yield Management." A competing 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 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 70 rooms and a standard deviation of 29 rooms. Assume that demand follows a Normal distribution around the forecast.
Find the optimal protection level for full price rooms (the number of rooms to be protected from sale at a discount price).