Problem 12-21 (Algorithmic) South Central Airlines operates a commuter flight between Atlanta and Charlotte. The plane holds 32 passengers, and the airline makes a $130 profit on each passenger on the flight. When South Central takes 30 reservations for the flight, experience has shown that, on average, two passengers do not show up. As a result, with 32 reservations, South Central is averaging 30 passengers with a profit of 30(130) = $3,900 per flight. The airline operations office has asked for an evaluation of an overbooking strategy in which the airline would accept 34 reservations even though the airplane holds only 32 passengers. The probability distribution for the number of passengers showing up when 34 reservations are accepted is as follows: Passenger Showing Up Probability 30 0.05 31 0.25 32 0.50 33 0.15 34 0.05 The airline will receive a profit of $130 for each passenger on the flight, up to the capacity of 32 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 $180 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. a. Does your simulation recommend the overbooking strategy? Yes What is the mean profit per flight if overbooking is implemented? Round your answer to the nearest dollar. Over $ 4071 b. Explain how your simulation model could be used to evaluate other overbooking levels, such as 33, 35, and 36, and for recommending a best overbooking strategy. The input in the box below will not be graded, but may be reviewed and considered by your instructor