Northwest Airlines runs daily flights from Detroit to Amsterdam. They face a fixed cost of $70,000 for each flight independent of the actual number of passengers on the plane. There are 310 seats available on a plane. One-way tickets generate revenues of $600 apiece when used but are fully refundable if not used. On a typical weekday, the airline estimates that the number of no-shows will range between 0 and 20; all intermediate values are equally likely.
By law, an airline is allowed to overbook flights, but must give compensation of $250 to all ticketed passengers not allowed to board. In addition, it must provide those passengers with alternative transportation on another carrier (the cost of providing the alternative transportation just wipes out the $600 revenue). How many tickets should Northwest book on its flight from Detroit to Amsterdam?