You have been asked to determine a policy for accepting reservations for an airline flight. This particular flight uses an aircraft with 15 first-class seats and 75 economy-class seats. First-class tickets on the flight cost $500 and economy-class tickets cost $250. The number of individuals who seek to reserve seats takes on the equally likely values of 10, 11,..., 20 in first class and the equally likely values 40, 41,..., 120 in economy class. The demand for first-class seats and that for economy-class seats are independent. The airline allows itself to sell somewhat more tickets than it has seats. This is a common practice called overbooking. You are asked to analyze the four possible booking policies which permit the overbooking of either up to 0, or up to 3 first-class seats and the overbooking of either up to 5, or up to 10 economy seats. Each passenger who buys a first-class seat has a 10% probability of not showing up for the flight. The probability of not showing up is 5% for economy-class passengers. Passengers decide whether to show up independently of each other. First-class passengers who do not show up can return their unused tickets for a full refund. No-shows in the economy class are not entitled to any refund. Any first-class passengers who show up for the flight but cannot be seated in the first class are entitled to a full refund plus $400 compensation. If there are free seats in first class and economy class is full, economy-class passengers can be seated in first class. If an economy-class passenger shows up and is denied a seat, however, they get a full refund plus $200 compensation. Use computer simulation to find for each of the four possible overbooking policies both the expected value of the net profit for the flight and the probabilities of the net profit falling in each of the ranges [$15,000, $16,000], . . . ,[$27,000, $28,000].