Problem 2: Overbooking Conundrum

Gamma Airline operates a red-eye flight from Kansas City to Seattle on Monday mornings. All seats for this flight scheduled next Monday have already been sold. However, given a forecast of inclement weather in Seattle starting Monday, the airline anticipates numerous last-minute cancellations. Specifically, it expects the number of cancellations to follow a normal distribution with a mean of 50 and a standard deviation of 40.

As a result, the airline plans to overbook the flight by selling additional tickets at a discounted price of $200 each. Assume that these discounted tickets will be sold immediately and all passengers who purchase them will show up on Monday. However, if more ticketed passengers show up than there are available seats, regulations require the airline to pay $500 in compensation to each passenger who cannot be accommodated.

Flag question: Question 8Question 81 pts

What is the optimal number of tickets that Gamma Airline should discount to maximize profit? If your answer is not an integer, provide at least three decimal places, e.g., 7.500.