Airline overbooking is a common practice. Many people makereservations on severa

Question

Airline overbooking is a common practice. Many people makereservations on several flights due to uncertain plans and thencancel at the last minute or simply fail to show up. Eagle Air is asmall commuter jet. Their planes hold only 6 people. Past recordsindicate that 20% of the people making a reservation do not show upfor the flight. We will assume that all reservations areindependent; that is, each reservation is for one person and thesereservations are made independent of one another. Suppose for eachempty seat the airline loses $150 and for each passenger who showsup and does not have a seat the airline must pay $125. The airlinecan make 6, 7, 8, or 9 reservations, how many reservations shouldthe airline make in order to minimize their total expectedcost?

Explanation / Answer

The number of people that a plane can hold is n = 6.

The percentage of people who don't show up is q= 0.20.

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