Problem $2.$ A hotel has $150$ rooms with standard Queen$-$size beds and two rates: a full price of $$250$ 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 average demand by business travelers has a mean of $70$ rooms and a standard deviation of $29$ rooms.

Assume that this demand follows a normal distribution. Find the optimal protection level for full price

rooms $($the number of rooms to be protected from sale at a discount price$)$ and the booking limit for discount

rooms, respectively.