Suppose a small plane can seat 20 passengers. Airlines often book more passengers than seats available knowing there is a good chance someone might cancel and the airline loses $250 for every empty seat. On the other hand, when they are overbooked and more people show up than there are seats available for them, they have to offer an incentive for passengers to reschedule and the incentive to get a passenger to give up a seat costs the airline $100 on average. How many seats should the airline sell in order to minimize their expected losses?

(Note: this is a question covering some of the material from Conditional Probability & Independence and/or Random Variables (from "A First Course in Probability" by Ross) so it may be tricky. Please explain in details, will reward THANKS)