Atlantic Air operates a low-cost passenger airline fleet of identical airplanes that provide 156 coach class seats each. Atlantic Air serves small airports through a hub-and-spoke network in which most Atlantic Air passengers fly to New York's JFK airport and then take a connecting flight to their destination. If flights are leav- ing a small airport, inbound to JFK, there is a 99% chance that all passengers will show up and board that flight, and a 1% chance that one of the passengers who has bought a ticket will not actually show up and take that flight. However, if the flight is leaving JFK, there is only a 95% probability that all passengers with tickets will board that flight, because delays of other flights arriving at JFK may cause some passengers to miss their connection at JFK. For flights leaving JFK, there is a 3% chance that one ticketed passenger may not show up for the flight, and a 2% prob- ability that two ticketed passengers may not show up and board that flight.

Atlantic Air has always sold 156 tickets for each of its flights, but is now interested in deliberately overbooking flights. Atlantic Air estimates that it can sell at least 158 tickets for any of its flights if it chose to. An empty seat on a flight represents a loss of \($200\) profit for Atlantic Air if there had been another passenger willing to pur- chase that seat. If Atlantic Air must "bump" a passenger from a flight because too many tickets were sold and too many passengers showed up to board, the company is willing to award the bumped passenger \($250\) in cash and book that passenger on a later flight; Atlantic Air considers this only \($250\) - \($200\) = \($50\) in direct expense after the profit on the delayed ticket is taken into consideration.

a. Taking the two types of loss into consideration, what is the expected loss on a flight leaving a small airport and arriving at JFK, under Atlantic Air's current policy of selling only 156 tickets?

b. Taking the two types of loss into consideration, what is the expected loss on a flight leaving JFK, under Atlantic Air's current policy of selling only 156 tickets?

c. Taking the two types of loss into consideration, what is the expected loss on a flight leaving JFK, if Atlantic Air sold exactly 158 tickets for that flight?

d. Determine the booking policy that minimizes these losses. How many tickets should Atlantic Air sell for a flight to JFK? How many tickets should Atlantic Air sell for a flight leaving JFK?