For all of the following simulation problems, provide a spreadsheet with the model and simulation. Provide simulation results as you think best and provide a written summary of your solution and findings from the simulation.

A ticket from Indianapolis to Orlando, Florida on AirSpiritWest Airlines sells for $150. The plane can hold 100 people. It costs AirSpiritWest $8000 to fly an empty plane. Each person on the plane incurs variable costs of $30 (for food and fuel). If the flight is overbooked, anyone who cannot get a seat receives $300 in compensation. On average, 95% of all people who have a reservation show up for the flight.

1. Run a simulation to determine how many reservations for the flight AirSpiritWest should book to maximize expected profit. NOTE: Assume that passengers who do not show can not get a refund.
2. Now suppose that AirSpiritWest has done some data analysis of past flights and they have determined that the actual amount of compensation paid to bumped passengers is random and the probability of ticketed travelers showing up is also random. AirSpiritWest tends to pay compensation to bumped passengers in vouchers and they either pay nothing in compensation, $100, $300 or $750 in vouchers depending on how upset passengers are (they pay the same amount to all passengers bumped from the same flight). By past data they have paid nothing 15% of the time, 45% of the time they have paid $100, 10% of the time they have paid $300, and 30% of the time they have paid $750. The probability of a ticketed traveler showing up for the flight is best modeled with a triangular distribution with minimum probability of 0.88, most likely probability of 0.98, and maximum probability of 0.99. Now how many reservations for the flight should AirSpiritWest book? How is this solution different from the original problem? Why do you guess that is?

1. The data analysis is not completely clear on one more point: correlation between the compensation paid and the probability of a ticketed traveler showing up. Some analysts are convinced that there is a positive correlation in the range of 0.4 while others are convinced its negative at -0.6. The argument for the positive correlation is that if the probability of showing up is high, then more passengers will get bumped so more passengers will be inconvenienced and angry and they will have to pay a higher compensation. The argument for the negative correlation is that if more passengers show up, then more people are bumped so travelers see that other people are also being bumped and they are more willing to accept a lower compensation since theyre not being singled out. The data analysis is not clear which way it goes and further tests are being run. However, the more extensive testing is going to take several weeks and you have to produce a report right now. What is the effect of correlation on the number of reservations that AirSpiritWest should book for the flight? How much difference does the negative versus positive correlation make? Why do you suspect it has this effect?