Most airlines practice Overbooking. That is they are willing to make more reservations than they have seats on an airplane. Why would they do this? The basic reason is simple; on any given flight a...

Most airlines practice Overbooking. That is they are willing to make more reservations than they have seats on an airplane. Why would they do this? The basic reason is simple; on any given flight a few passengers are likely to be “no-shows” if the airline overbooks slightly, then it still may be able to fill the airplane. Of course, this policy has its risk. If more passengers arrive to claim their reservations than there are seats available, the airline must “bump” some of its passengers. Often this is done by asking for volunteers. If a passenger with a reserved seat is willing to give up his or her seat, the airline typically will give a refund as well as provide a free ticket to the same or another destination. The fundamental trade –off is weather the additional expected revenue gained by flying an airplane that is nearer to capacity on average is worth the additional expected cost of refunds and free tickets. To study the overbooking policy, let us look at the hypothetical situation. Mockingbird Airlines has a small commuter airplane with places for 16 passengers. The airline uses this jet on a route for which it charges $225 for one way fare. Every flight has a fixed cost of $900 (for pilot’s salary, fuel, airport fees, and so on). Each passenger costs Mockingbird and additional $100. Finally, the “no-show” rate is 4%. That is on average approximately 4% of those passengers holding confirmed reservations do not show up. Refunds for unused tickets are made only if the reservation is cancelled at least 24 hours before scheduled departure. How many reservations should mockingbird be willing to sell on this airplane? The Strategy will be to calculate the expected profit for a given number of reservations. For example, suppose that the Mockingbird Manager decides to sell 18 reservations. The revenue is $225 times the number of reservations: R=$225(18) =$4050 The cost consists of two components. The first is the cost of flying the plane and...