The Inn at Penn hotel has 150 rooms with standard queen-size beds and two rates: a full price of $300 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). For a particular Tuesday night, the hotel estimates that the demand from leisure travelers could fill the whole hotel with a normal distribution with a mean 1000 and a standard deviation of 100. Historically, the hotel estimates that the demand from business travelers is distributed normally with a mean of 70 rooms and a standard deviation of 29. Find the optimal booking limitfor discount rooms.