Skyhigh Airlines flight 708 from New York to Los Angeles is a popular flight that is usually sold out.

Skyhigh Airlines flight 708 from New York to Los Angeles is a popular flight that is usually sold out. Unfortunately, some ticketed passengers change their plans at the last minute and cancel or re-book on another flight. Subsequently, the airline loses the $450 for every empty seat that the plane flies.

To limit their losses from no-shows, the airline routinely overbooks flight 708, and hopes that the number of no-shows will equal the number of seats oversold. However, things seldom work out that well. Sometimes flight 708 has empty seats, and other times there are more passengers than the airplane has seats. When the latter happens, the airline must "bump" pre-ticketed passengers; they estimate that this will cost them $275 in later accommodations to bumped passengers.

Fortunately for the airline, hopeful passengers usually show up at flight time without tickets and want to get on the flight. The airline classifies these passengers as standbys while it waits to determine how many seats, if any will be available. Standby passengers can help offset the loss associated with flying an empty seat, but the airline suffers no penalty when a standby passenger is not able to receive a seat.

Airline records indicate that the number of No-shows and Standbys will vary according to the probability tables below:

           Number of    Relative                                 Number of    Relative

           No-shows      Frequency                             Standbys      Frequency

                  0                0.04                                           0                0.26

                  1                0.08                                           1                0.34

                  2                0.14                                           2                0.24

                  3                0.25                                           3                0.11

                  4                0.30                                           4                0.05

                  5                0.13

                  6                0.06

Simulate 25 flights with each of several different overbooking decisions (assume that the best overbooking number will be between 1 and 6) to determine the optimal number of seats to overbook this flight, to minimize the airline's losses. Tabulate your results and use them to justify your recommendations. You should report, for each scenario, the average loss per flight, and the percentage of flights that suffer a loss.