Next week, Super Discount Airlines has a flight from New York to Los Angeles tha

Question

Next week, Super Discount Airlines has a flight from New York to Los Angeles that will be booked to capacity. The airline knows from past history that an average of 32 customers (with a standard deviation of 22) cancel their reservation or do not show for the flight. Revenue from a ticket on the flight is $130. If the flight is overbooked, the airline has a policy of getting the customer on the next available flight and giving the person a free round-trip ticket on a future flight. The cost of this free round-trip ticket averages $258. Super Discount considers the cost of flying the plane from New York to Los Angeles a sunk cost.

By how many seats should Super Discount overbook the flight? (Round your answer to the nearest whole number.)

By how many seats should Super Discount overbook the flight? (Round your answer to the nearest whole number.)

Explanation / Answer

21 seats

p - regular seats

x-overbooked seats

y-passengers don't show up

cost function: (p+x)*130 - (x-y)*258

or,p*130 + x*388-y*258

it would be minimum for x= (258/388)y

taking mean y , we get x = 21 seats

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