The Inn at Penn 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). 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 70 rooms and a standard deviation of 29.

a. Find the optimal protection level for full-price rooms (the number of rooms to be protected from sale at a discount price).

b. What number of rooms (on average) remains unfilled if we establish a protection level of 61 for the full-price rooms?

c. If The Inn protects 50 rooms for the full price, what is The Inns expected revenue?

Other than calculations, it would be the best to also give me input values (in red colour ) for the excel template. Thanks a lot, will give thumbs up for any answers!