Problem 12-21 (Algorithmic)

South Central Airlines operates a commuter flight between Atlanta and Charlotte. The plane holds 29 passengers, and the airline makes a $100 profit on each passenger on the flight. When South Central takes 27 reservations for the flight, experience has shown that, on average, two passengers do not show up. As a result, with 29 reservations, South Central is averaging 27 passengers with a profit of 27(100) = $2,700 per flight. The airline operations office has asked for an evaluation of an overbooking strategy in which the airline would accept 31 reservations even though the airplane holds only 29 passengers. The probability distribution for the number of passengers showing up when 31 reservations are accepted is as follows:

Passenger Showing Up	Probability
27	0.05
28	0.25
29	0.50
30	0.15
31	0.05

The airline will receive a profit of $100 for each passenger on the flight, up to the capacity of 29 passengers. The airline will also incur a cost for any passenger denied seating on the flight. This cost covers added expenses of rescheduling the passenger as well as loss of goodwill, estimated to be $150 per passenger. Develop a worksheet model that will simulate the performance of the overbooking system. Simulate the number of passengers showing up for each of 500 flights by using the VLOOKUP function. Use the results to compute the profit for each flight.

1. Does your simulation recommend the overbooking strategy? (YES OR NO) What is the mean profit per flight if overbooking is implemented? Round your answer to the nearest dollar. Over $ ___

0.7609 0.9636 0.7910 0.2083 0.6918 0.3680 0.1092 0.1961 0.7305 0.5340 0.3901 0.0638 0.7303 0.0931 0.2691 0.0790 0.9540 0.9784 0.5683 0.5629 0.0142 0.2540 0.2137 0.0285 0.0276 0. 8772 0.6414 0.7377 0.3562 0.5004 0.5034 0.6695 0.5202 0.9235 0.7742 0. 8050 0.1293 0.5760 0.5862 0.1639 0.3210 0.1101 0.0575 0.7789 0.6562 0.9577 0.3554 0.0106 0.9066 0.5064 0.3657 0.0552 0.9447 0.1991 0.5464 0.9210 0.9754 0.7977 0.7828 0.9241 0.3892 0.3578 0.7979 0.8337 0.6586 0.4875 0.8257 0.6829 0.6247 0.3210 0.2606 0.4733 0.3790 0.3153 0.2194 0.0905 0.7609 0.9636 0.7910 0.2083 0.6918 0.3680 0.1092 0.1961 0.7305 0.5340 0.3901 0.0638 0.7303 0.0931 0.2691 0.0790 0.9540 0.9784 0.5683 0.5629 0.0142 0.2540 0.2137 0.0285 0.0276 0. 8772 0.6414 0.7377 0.3562 0.5004 0.5034 0.6695 0.5202 0.9235 0.7742 0. 8050 0.1293 0.5760 0.5862 0.1639 0.3210 0.1101 0.0575 0.7789 0.6562 0.9577 0.3554 0.0106 0.9066 0.5064 0.3657 0.0552 0.9447 0.1991 0.5464 0.9210 0.9754 0.7977 0.7828 0.9241 0.3892 0.3578 0.7979 0.8337 0.6586 0.4875 0.8257 0.6829 0.6247 0.3210 0.2606 0.4733 0.3790 0.3153 0.2194 0.0905