Problem 12-21 (Algorithmic) South Central Airlines operates a commuter flight between Atlanta and Charlotte. The plane holds 30 passengers, and the airline makes a $110 profit on each passenger on the flight. When South Central takes 28 reservations for the flight, experience has shown that, on average, two passengers do not show up. As a result, with 30 reservations, South Central is averaging 28 passengers with a profit of 28(110) = $3,080 per flight. The airline operations office has asked for an evaluation of an overbooking strategy in which the airline would accept 32 reservations even though the airplane holds only 30 passengers. The probability distribution for the number of passengers showing up when 32 reservations are accepted is as follows Passenger Showing Up 28 29 30 31 32 Probability 0.05 0.25 0.50 0.15 0.05 The airline will receive a profit of $110 for each passenger on the flight, up to the capacity of 30 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 $160 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