Granite State Airlines serves the route between New York and Portsmouth, New Hampshire, with a single-flight-daily 100-seat aircraft. The one-way fare for discount tickets is $100, and the one-way fare for full-fare tickets is $150. Discount tickets can be booked up until one week in advance, and all discount passengers book before all full-fare passengers. Over a long history of observation, the airline estimates that full-fare demand is normally distributed, with a mean of 56 passengers and a standard deviation of 23, while discount-fare demand is normally distributed, with a mean of 88 passengers and a standard deviation of 44.

a. A consultant tells the airline it can maximize expected revenue by optimizing the booking limit. What is the optimal booking limit?

b. The airline has been setting a booking limit of 44 on discount demand, to preserve 56 seats for full-fare demand. What is its expected revenue per flight under this policy? (Hint: Use a spreadsheet.)

c. What is the expected gain from the optimal booking limit over the original booking limit?

d. A low-fare competitor enters the market and Granite State Airlines sees its discount demand drop to 44 passengers per flight, with a standard deviation of 30.

Full-fare demand is unchanged. What is the new optimal booking limit?