1. ) Consider a specific airline flight on a specific day with a fixed number n of seats. (You can also think of a hotel with a specific number of rooms available for a specific night). Let p denote the return the airline receives for each seat that is occupied that flight. (The airline receives returns only for occupied seats, not for reservations made.) If the airline overbooks the flight and m passengers show up for the flight with confirmed reservations and m > n, then there are m n actual overbookings, and the airline occurs a cost of > 0 (and receives no returns) for each one of them. The airline wishes to specify the booking level y as the number of seats that can be booked in advance for that flight. In particular, the airline plans to set y strictly greater than n. The first y requests for a reservation on the flight will be given a confirmed reservation and any after will be told that the flight

is full.

Let Z be the random number of no-shows for the flight: the number of people with confirmed reservation on the flight who, for whatever reason, do not show up for it. All no-shows get their money back. For convenience, assume that no more than n no-shows will occur. Assume that Z follows a normal distribution truncated at 0 and n. The mean is n/10 and standard deviation is n/50.

Note that this problem can be treated as a news vendor problem. The customers with confirmed reservations showing up are the demand. Let us assume that n = 100. If p = 3,000 dollars and = 1,000 dollars, how many seats y should be sold?

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