12. South Central Airlines (SCA) operates a commuter flight between Atlanta and Charlotte. The regional jet holds 50 passengers, and currently SCA only books up to 50 reservations. Past data show that SCA always sells all 50 reservations, but on average, two passengers do not show up for the flight. As a result, with 50 reservations the flight is often being flown with empty seats. To capture additional profit, SCA is considering an overbooking strategy in which they would accept 52 reservations even though the airplane holds only 50 passengers. SCA believes that it will be able to always book all 52 reservations. The probability distribution for the number of passengers showing up when 52 reservations are accepted is estimated as follows: Passengers Showing Up 48 49 50 51 52 Probability 0.05 0.25 0.50 0.15 0.05 SCA receives a marginal profit of $100 for each passenger who books a reservation (re- gardless whether they show up or not). The airline will also incur a cost for any passenger denied seating on the flight. This cost covers added expenses of rescheduling the passen- ger as well as loss of goodwill, estimated to be $150 per passenger. Develop a spreadsheet simulation model for this overbooking system and simulate the number of passengers that show up for a flight a. What is the average net profit for each flight with the overbooking strategy? b. What is the probability that the net profit with the overbooking strategy will be less than the net profit without overbooking (50*$100 = $5000)? c. Explain how your simulation model could be used to evaluate other overbooking levels such as 51, 53, and 54 and for recommending a best overbooking strategy