Every day, several million people around the world travel by plane. For several reasons a certain percentageof booked passengers does not show up in time for departure. The plane will then depart not charged to its capacity. The airline could have sold more tickets. [br]Airlines gather and analyze large amount of data over many years to make a reasonable prediction about the probability of a no-show for a certain route on a certain time. In anticipation of no-shows, airlines sell more tickets than physical seats available and hope that the amount of passengers showing up ideally fills exactly the plane.[br]It happens that more passengers arrive for departure than the capacity of the plane leading to one or more passengers being bumped and thus unable to take the flight for which they had reservations.[br]Airlines deal with bumped passengers in various ways. Some are accommodated in hotels, others are given some kind of cash or airline ticket incentive. This means financial loss for the airline and a damaged reputation.[br]How can math help finding the number of tickets beyond capacity that an airline should sell in order to maximize the company’s revenue?[br][br][br][br][br][br]