An aircraft has 100 seats, and there are two types of fares: full ($499) and discount ($99).

a) While there is unlimited demand for discount fares, demand for full fares is estimated to be Poisson with mean l=20 (the table below gives the distribution function). How many seats should be protected for full-fare passengers?

b) An airline has found that the number of people who purchased tickets and did not show up for a flight is normally distributed with mean of 20 and standard deviation of 10. The airline estimates that the ill will and penalty costs associated with not being able to board a passenger holding confirmed reservation are estimated to be $600. Assume that opportunity cost of flying an empty seat is $99 (price that discount passenger would pay). How much should airline overbook the flight?