II. San Francisco Express Airlines, SaFE for short, flies from PHL to SFO. On a Thursday evening flight, the number of last-minute no-shows and cancellations is normally distributed with mean of 18 and a standard deviation of 5. SaFE has an unlimited number of low fare travelers who pay $375. The cost of bumping such a passenger is estimated to be $500 (due to lost good will as well as the cost of routing their itinerary through other airlines). SaFE offers this low fare of $375 because it also comes with a cancellation/rebooking fee of $150 if a customer does not show up for the flight or cancels her reservation, she must pay $150 to use the ticket on another flight. (Hint: this information concerning the rebooking fee is for information purposes only and does not affect the cost of being overstocked or understocked in your analysis). Assume that the plane has a capacity of 200.

a. To maximize revenue from this flight, how many seats should the airline overbook? b. What is the expected number of passengers that will be bumped given the overbooking decision? c. What is the expected profit from the overbooking decision? d. Customers are more reliable on the Friday evening flight. On that flight, the average number of no shows and cancellations is normally distributed with a mean of 7 and a standard deviation of 2. Suppose SaFE overbooks that flight by 6 seats. What is the probability that at least 1 passenger will be bumped from this flight?