Offwefly Airlines has a daily flight from Sacramento to Las Vegas with a capacit

Question

Offwefly Airlines has a daily flight from Sacramento to Las Vegas with a capacity of 100 passengers. On average, 12 ticket holders cancel their reservations at the last minute, so the company intentionally overbooks the flight. Cancellations can be described by a normal distribution with a standard deviation of 4.8. Profit per passenger is $100. If a passenger arrives but cannot board due to overbooking, the company policy is to provide compensation of $91.

What is the optimal probability of having one or more empty seats on the plane?

Explanation / Answer

Number of tickets, X = 100

Number of last-minute cancellations, n = 12

Overbooking cost , Co = $ 91

Underbooking cost, Cu = $ 100

Q = overbooking quantity

Probability (Q>N) = 100 / (91+100) = 100/191 = 0.5235

So , probability that no-shows is greater than over-book quantity = 0.4765 = 47%

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