South Central Airlines (SCA) operates a commuter flight between LAX and Denver. The airplane holds 50 passengers, and currently SCA sells up to 50 tickets. Past data shows that SCA always sells all 50 available tickets but, on average, two passengers do not show up. As a result, even though 50 tickets are sold, the flight is often being flown with empty seats. To capture additional profit, SCA is considering an overbooking strategy in which they would sell 52 tickets even though the airplane holds only 50 passengers. SCA believes that it will be able to always sell all 52 tickets.

SCA receives a marginal profit of $100 for each passenger who buys the ticket (regardless of whether or not they show up). The airline will also incur a cost for any passenger denied seating on the flight which is on average $250. This cost includes the added expenses of rescheduling the passenger as well as a negotiated compensation amount to be paid to the customer for their inconvenience. Develop a spreadsheet simulation model for this overbooking system that calculates the total profit for any given number of passengers that show up.

Passengers Showing Up	Probability
48	0.05
49	0.25
50	0.50
51	0.15
52	0.05

SCA knows that the cost of overbooking per passenger is going to be uncertain as it might be able to negotiate different amounts with different passengers. It is estimated that when there is any customer overbooked, the TOTAL cost of overbooking is normally distributed with a mean equal to 350*number of overbooked customers, and a standard deviation of 100*square root of number of overbooked customers. Implement this information in your simulation model.

USE EXCEL AND SHOW WORK

Question 1: What would be the average profit when uncertainty in overbooking cost is incorporated?

Question 2: What is the average profit whenever overbooking does happen?