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Overbooking Problem Conditions: Price of ticket = -x+500 Question: There are only 184 seats in the Boeing 737 plane.

Overbooking Problem

Conditions: Price of ticket = -x+500

Question:

There are only 184 seats in the Boeing 737 plane. The previous record shows that about 10% of passengers who are scheduled to take this flight fail to show up. And to find a volunteer that wishes to postpone his/her fight at the gate, the airline needs to pay $800.

a) If the airline sells 220 tickets, show that the expected profit is lower than not overselling. [Hint: use the Central limit Theorem and consider the 3σ interval].

b)[Bonus question] Estimate the maximum number of tickets, up to which the airline will profit by overselling.

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