The Inn at Penn hotel has 110 rooms with standard queen-size beds and two rates: a full price of $170 and a discount price of $100. 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). For a particular Tuesday night, the hotel estimates that the demand from leisure travelers could fill the whole hotel while the demand from business travelers is distributed normally with a mean of 80 rooms and a standard deviation of 20. Find the optimal protection level for full-price rooms (the number of rooms to be protected from sale at a discount price).