An airline sells 120 tickets for a flight that seats 100. Each ticket is non-ref

Question

An airline sells 120 tickets for a flight that seats 100. Each ticket is non-refundable and costs $200. The unit cost of flying a passenger (fuel, food, etc.) is $80. If the flight is overbooked, each person who does not find a seat is given $300 in cash. Assume it is equally likely that any number of people between 91 and 120 show up for the flight. Rounded to the nearest thousand (e.g., 18500 rounds to 19000), on the average how much expected profit (ignoring fixed cost) will the flight generate? Enter just the number; e.g., 11000

Explanation / Answer

If it is equally likely that 91 to 120 people will show up, then on average, you will have (91+120)/2 or 105.5 people show up. Since that is more than 100, you will, on average, generate (200-80)*100 profit less what you have to refund to the 5.5 people over 100.

Profit = (200*105.5)-(80*100)-(300*5.5)

= 21100-8000-1650

= 11450 $

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