(20 points) Triangle Airlines serves the route between New York and Bermuda with a single- flight-daily 120-seat aircraft. The one-way fare for discount ticket 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 that she can maximize expected revenue by optimizing the booking limit. What is the optimal protection level for full-fare passengers? (b) Is the expected revenue convex or concave with respect to the protection level? (no need to prove it) (c) The airline has been setting a booking limit of 44 on discount demand, to preserve 56 seats for full-fare demand. What is the expected revenue per-flight from low-fare demand? (d) Suppose the airline offers ultra-discount tickets for $80, and ultra-discount tickets can be booked up until one month in advance, before any discount passenger booking. Ultra- discount fare demand is normally distributed with a mean of 20 and a standard deviation of 10. Find the booking limits using the EMSR-a heuristic. (20 points) Triangle Airlines serves the route between New York and Bermuda with a single- flight-daily 120-seat aircraft. The one-way fare for discount ticket 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 that she can maximize expected revenue by optimizing the booking limit. What is the optimal protection level for full-fare passengers? (b) Is the expected revenue convex or concave with respect to the protection level? (no need to prove it) (c) The airline has been setting a booking limit of 44 on discount demand, to preserve 56 seats for full-fare demand. What is the expected revenue per-flight from low-fare demand? (d) Suppose the airline offers ultra-discount tickets for $80, and ultra-discount tickets can be booked up until one month in advance, before any discount passenger booking. Ultra- discount fare demand is normally distributed with a mean of 20 and a standard deviation of 10. Find the booking limits using the EMSR-a heuristic