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Revenue Management $(10$ points$)$:

The Inn at Baltimore 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. For a particular Tuesday night, the hotel estimates that the demand from the 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$)$ remain unfilled if we establish a protection level of $61$ for the full$-$priced rooms?

Due to customer no$-$shows, The Inn at Baltimore hotel is considering implementing overbooking. Recall from previous problem that the Inn Baltimore hotel has $150$ rooms, the full fare is $$200,$ and the discount fare is $$120.$ The forecast of no$-$shows is Poisson

$2$

with a mean of $15\mathrm{.}5.$ The distribution and loss function of that distribution are as follows:

$\backslash$table$[[Y,F(Y),L(Y)$