Allegiant Airlines is considering an overbooking policy for one of its flights. The airplane has 50 seats, but Allegiant is considering accepting more reservations than seats because sometimes passengers do not show up for their flights, resulting in empty seats. The Data worksheet in the file overbooking contains data on 1,000 passengers showing whether they showed up for their respective flights.

In addition, Allegiant has conducted a field experiment to gauge the demand for reservations for the current flight. During this experiment, they did not limit the number of reservations for the flight to observe the uncensored demand. The following table summarizes the result of the field experiment.

Allegiant receives a marginal profit of $100 for each passenger who books a reservation (regardless of whether they show up). Allegiant incurs a rebooking cost of $300 for each passenger who books a reservation, but is denied seating due to a full airplane; this cost results from rescheduling the passenger and any loss of goodwill.

a. Model the number of booked passengers who show up for their flight as a binomial random variable. Describe how to determine the two parameters (n and p) for the binomial distribution in this application. Hint: Review Appendix 13.1 for description of the binomial distribution and consider the the data in the Data worksheet of the file overbooking.

b. The number of reservations demanded is a random variable. How should it be modeled?

c. To control its rebooking costs, Allegiant wants to set a limit on the number of reservations it will accept. Evaluate Allegiant’s average net profit for reservation limits of 50, 52, and 54, respectively. Based on the 95% confidence intervals for average net profit, which reservation limit do you recommend?

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Number of Reservations Demanded Probability 48 0.05 49 0.05 50 0.15 51 0.30 52 0.25 53 0.10 54 0.10