The ticket price for an OKC-Houston flight is $150. Each plane can hold up to 100passengers. Usually, some of the passengers who have purchased tickets for a flight fail to show up (no shows). Assume that anybody who does not use a ticket gets $150 refund. To protect against no-shows, the airline will try to sell more than 100 tickets for each flight. Any ticketed customer who is unable to board the plane due to its capacity being reached is entitled to compensation of $100. Past data indicate that the number of no-shows for OKC-Houston flight, D, is normally distributed with a mean of 15 and a standard deviation of 5 customers. To maximize expected revenue less compensation costs, how many tickets should the airline sell for each flight?
Let q denote the number of tickets sold for the flight and d the actual number of no shows. Hence q-d is the number of customers actually showing up to board the plane which can be less than or equal to or greater than the capacity of the plane, which is 100.