A newly created NorthEast Airways (NE) flight from Philadelphia to Boston has 300 seats. The high fare on the flight is $800 and the restricted low fare is $300. There is ample demand for the low fare class but high fare demand is random. Furthermore, the customers who buy low fare buy their tickets well in advance before high fare customers. Assume the demand for the high fare is normally distributed with a mean 120 and a standard deviation of 50.

1. Due to the problem of passenger no-shows, Mr. Wright decides to overbook the flight. He estimates that his loss from a passenger holding a valid reservation who is denied a seat is $550. He also estimates that the number of passengers with reservations who are no-shows is Poisson with a mean of 9.25. What is Mr. Wright's optimal overbooking quantity?

2. Suppose Mr. Wright chooses to overbook by 8. Assume that the number of passengers with reservations who are no-shows is Poisson with a mean of 9.25. What is the probability of bumping at least one (i.e., one or more) customers?

3. Suppose instead that Mr. Wright overbooked by 6. Assume as before that the number of passengers with reservations who are no-shows is Poisson with a mean of 9.25. What is the probability that the flight has at least two (i.e., two or more) empty seats?