Consider a flight of an A380 with 600 seats, and a fare of $320. Assume that the no-shows follow a normal distribution with an expected number of no-shows of 30 with standard deviation 10. At the check-in counter several passengers might need to be bumped because the plane is overbooked, and too many passengers show up. Furthermore, assume that bumped passengers need to wait more than two hours to get another flight with the same airline. The Department of Transportation has a policy for this case of involuntary denied boarding: If the substitute transportation is scheduled to get you to your destination more than two hours later or if the airline does not make any substitute travel arrangements for you, the compensation doubles (200% of your fare, but $400 maximum). The ticket price will not be refunded, and all bumped passengers will use their tickets for later flights of the same airline. What is the optimal booking limit, i.e. how many reservations should you take?