On a given flight there are 200 seats. Suppose the ticket price is $475 for each

Question

On a given flight there are 200 seats. Suppose the ticket price is $475 for each seat, and the number of passengers who reserve a seat but do not show up for departure is normally distributed with mean 30 and standard deviation 15. You decide to overbook the flight and estimate that the average loss from a passenger that will have to be "bumped" (if the number of passengers exceeds the number of seats) is $800 (in addition to refunding the original ticket price). What is the maximum number of reservations that should be accepted?

Explanation / Answer

No of seatsin flight - 200

Ticket price -$475

Clearly 200 reservation can be arranged easily.Let they reserved for more than P ,number of reservation ( P> 200)

Marginal benefit 475 =R [Number of Not appearing> (P 200)] = 475 · (1 R[Number of Not Appearing (P 200)])

Equating the marginal benefit and the marginal cost ( 800). Q showing probability.

475 · (1 Q[Number of Not appearing (R 200)) = 800 · Q[Number of Not appearing (R 200)]

Q[Number of Not appearing (R 200)] = 475 / (800 + 475) = 0.3725. Then, the z value should be z = 0.32, and thus we obtain that (R 200) = 30 + (0.32)(15) = 25.2.

Thus maximum number of reservation is 200+25.2= 225.2

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