Air Montreal flight AM-1660 travels from Montreal to Toronto. The airplane assigned to the flight is an Airbus A319 having 125 seats. All of the seats are coach class. There is no first-class section. On the other hand, the airline sells two types of tickets discount, and full-fare. Discount tickets cost $400 each and must be purchased at least twenty-one days ahead of time. Full-fare tickets cost $1000 each, are refundable, and are available up to the time of departure on a space-available basis. Virtually all full-fare tickets are sold within twenty-one days before departure. The airline is trying to decide how many seats to set aside for full-fare passengers on its busy Monday morning flight. The seat inventory control policy follows a nested structure. That is, when discount tickets are offered, full-fare tickets must also be offered. A protection level can be established to "protect" seats for full-fare customers. The protected seats for full-fare customers are only available to full-fare customers. If too many seats are set aside for the full-fare customers, the airplane may depart with many empty seats should the demand be low. If too few seats are set aside, revenues again may be low due to the number of high-paying passengers being turned away because too many discount tickets were sold. The airline has estimated the demand for all two types of tickets. The demand distributions are all normal. The means and standard deviations are reported in the following table. In addition, the demands for the two types of tickets are assumed to be independent. Type Discount Full Mean Standard deviation 120 30 20 10 To simplify the problem, assume the demand for the two types arrive sequentially with discount first and full-fare last. Air Montreal wishes to determine how many seats to set aside for full-fare in order to maximize the expected revenue from flight AM-1660. (a) Construct a simulation model in Excel to simulate the following policy: protect 30 seats exclusively for full-fare customers. Simulate for 1000 times. What are the mean and standard deviation of the revenue? Calculate the 95% confidence interval for the mean. What do you think about the policy? (b) Optimize the mean of the revenue by varying the protection level for full-fare customers between 20 and 40. Report and plot all the results (the mean of the revenue with the confidence interval). Report the mean and standard deviation of the revenue corresponding to the optimal policy. Calculate the 95% confidence interval for the mean of the revenue corresponding the optimal policy. (c) Find the 95% confidence interval for the probability of optimal revenue greater than or equal to the mean revenue that corresponds to protection level of 30 seats (i.e., the mean revenue that you found in part a).