Problem 1 (28 points, 4 points for each part).

Overbooking and bumping of ticketed passengers by commercial airlines have been a focus of news outlets during much of 2017. In this problem, we will consider an over-booking problem of Unplugged Airlines flying the MCI-SFO flight leg. The airline operates Airbus A310 with 200 seats, and that the average ticket price for this flight is $475.00. For the reasons of simplicity, assume that there is only one fare class. The number of passengers who book a seat but do not show up for departure is normally distributed with a mean of 30 and a standard deviation of 15. You, as the reservations manager, decide to overbook the flight. You estimate that the average loss form a passenger who will have to be bumped (if the number of passengers exceeds the number of seats) is $800

1. (4 points) What is the maximum number of reservations that should be accepted given there are 200 seats?
2. (4 points) Suppose you allow 220 reservations. How much money do you expect to pay out in compensation to bumped passengers?
3. (4 points) Suppose you allow 220 reservations. What is the probability that you will have to deal with bumped passengers?

Next, assume the available capacity is still 200 seats but Unplugged no longer allows overbooking due to bad press. It instead sets two fare classes: the high fare at $675.00, and the low fare at $375.00. Demand for the low fare is abundant while demand for the high fare is normally distributed with a mean of 80 and a standard deviation of 35.

1. (4 points) What is the probability of selling 200 reservations or more if you set an optimal protection level (i.e., the number of sets to "protect" for high fare customers) for the full fare?
2. (4 points) Suppose a protection level of 85 is established. What is the average number of lost high-fare passengers?
3. (4 points) Continue to assume a protection level of 85 is established. What is the expected number of unoccupied seats?
4. (4 points) Again assume a protection level of 85 is established. What is the expected revenue from the flight?