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, 15 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 2. Profit per passenger is $64. If a passenger arrives but cannot board due to overbooking, the company policy is to provide compensation of $84. What is the optimal probability of having one or more empty seats on the plane? Carry answer to 4 decimal places.

Explanation / Answer

Underage cost = Cu = profit per passenger = $64

Overage cost = Co = cash payment per passenger = $ 84

Thus , Critical ratio = Cu / Cu + Co = 64 / ( 64 + 84) = 64 / 148 = 0.4324

Corresponding Z value for above Critical Ratio = NORMSINV ( 0.4324) = -0.1703( -0.17 ROUNDED TO 2 DECIMAL PLACES )

Thus, number of tickets to be overbooked

= Mean value of cancellation + Z x Standard deviation of cancellation

= 15 -0.17 x 2

= 15 -0.34

= 14.66( 15 rounded to nearest whole number )

OVERBOOKED = 15 TICKETS

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