(Overbooking The Inn at Penn) Due to customer no-shows, The Inn at Penn hotel is considering…

(Overbooking The Inn at Penn) Due to customer no-shows, The Inn at Penn hotel is considering implementing overbooking. Recall from Q15.1 that The Inn at Penn has 1 50 rooms, the full fare is $200, and the discount fare is $120. The forecast of no-shows is Poisson with a mean of 1 5.5. 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 I SO rooms that The Inn should accept?

b. If The Inn accepts 1 60 reservations, what is the probability The Inn will not be able to honor a reservation?

c. If The Inn accepts 1 65 reservations, what is the probability The Inn will be fully occupied?

d. If The Inn accepts 1 70 reservations, what is the expected total cost incurred due to bumped customers?