Granite State Airlines serves the route between New York and Portsmouth, NH, 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 they can maximize expected revenue by optimizing the booking limit. What is the optimal booking limit? (Hint: Use the standard normal cumulative distribution table)

b) The airline has been setting a booking limit of 44 on discount demand, to preserve 56 seats for full-fare demand. What is their expected revenue per flight under this policy? (Hint: First find the expected revenue when b= 0. Here you can assume Probability{df = k} = Ff(k+0.5) – Ff(k-0.5) and use a spreadsheet. Then using the recursive formula, find the expected revenue if b is increased by 1 until it reaches b=44 using a spreadsheet)

c) What is the expected gain from the optimal booking limit over the original booking limit?7