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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 25 customers (with a standard deviation of 15) cancel their reservation or do not show for the flight. Revenue from a ticket on the flight is \(125. If the flight is overbooked, the airline has a policy of getting the customer on the next available flight and giving the person a free round-trip ticket on a future flight. The cost of this free round-trip ticket averages \)250. 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?

Step by step solution

01

Calculation of probability(P) of tickets being not sold by customers

$$\begin{gathered} \text{P =}\frac{\text{Cc}}{\text{Cc + Ce}} \\ =\frac{\$125}{\$125+\$250} \\ =\$0.33 \end{gathered}$$

02

 Calculation of number of seats overbooked booked

By using the Probability(P) of tickets are not being sold = 0.33

Standard deviation = 25

Average customers = 15

Calculation of Z (inverse of normal distribution curve)

NORMINV (0.3333)(Excel spreadsheet) = -0.4308

When the value of Z is negative then it indicates tickets are overbooked but less than 25.

$$\begin{gathered} Numberofseatsoverbooked=Z×S\tan darddeviation \\ =-0.4308×15 \\ =-6.462 \end{gathered}$$

03

Calculation of the number of seats booked in the airlines 

Given,

Average seats booked = 25

Overbooked seats by customer = -6.462

$$\begin{gathered} Numberofseatsbooked=Averageseatbooked+Overbookedseats=25+(-6.462) \\ =25-6.462 \\ =18.538or19 \end{gathered}$$

So, the total number of seats booking offered by the Airlines is 19 seats

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