Question: Due to customer no shows The Inn at Penn hotel is

Due to customer no-shows, The Inn at Penn hotel is considering implementing overbooking. Recall from Q16.1 that The Inn at Penn has 150 rooms, the full fare is $200, and the discount fare is $120. The forecast of no-shows is Poisson with a mean of 15.5. The distribution and loss functions of that distribution are as follows:
The Inn is sensitive about the quality of service it provides alumni, so it estimates the cost of failing to honor a reservation is $325 in lost goodwill and explicit expenses.
a. What is the optimal overbooking limit, that is, the maximum reservations above the available 150 rooms that The Inn should accept?
b. If The Inn accepts 160 reservations, what is the probability The Inn will not be able to honor a reservation?
c. If The Inn accepts 165 reservations, what is the probability The Inn will be fully occupied?
d. If The Inn accepts 170 reservations, what is the expected total cost incurred due to bumped customers?

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