Problem 12-21 (Algorithmic) South Central Airlines operates a commuter ight between Atlanta and Charlotte. The plane holds 30 passengers, and the airline makes a $100 profit on each passenger on the ight. When South Central takes 28 reservations for the ightr 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 prot of 28(100) = $2,800 per ight. The airline operations ofce has asked for an evaluation of an overbooking strategy in which the airline would aocept 32 reservations even though the airplane holds ()an 30 passengers. The probability distribution for the number of passengers showing up when 32 reservations are aocepted is as follows: Passenger Showing Up Probability 23 [1.05 29 0.25 30 [1.50 31 0.15 32 [1.05 The airline will receive a prot of $1DU for each passenger on the ight. up to the capacity of 30 passengers. The airline will also incur a cost For any passenger denied seating on the ight. 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 ights by using the VLOOKUP function. Use the results to compute the prot for each ight. a. Does your simulation recommend the overbooking strategy? 7 What is the mean prot per ight if overbooking is implemented? Round your answer to the nearest dollar. b. Explain howI your simulation model could he used to evaluate other overhooking levels, such as 31r 33, and 34, and for recommending a pest overhooking strategy. The input in the box below will not be graded. but may be reviewed and considered by your instructor