JetRed Airways flies several daily flights from Philadelphia to Chicago. Based on historical data, the flight on Wednesday evening before Thanksgiving is always sold out. However, there are usually no-shows so the airline decides to improve revenues by overbooking. The no-shows are Poisson-distributed with mean 8 and the airline estimates that the cost of bumping a passenger is about 10 times more than ticket price.
a. How many seats should JetRed overbook?
b. JetRed management is dreading bad publicity around Thanksgiving so it decides instead that it does not want to bump passengers more than 5% of the time. What is the maximum number of seats that JetRed can overbook?
c. Suppose 6 seats are overbooked. How many seats can JetRed expect to have empty, on average?