Alpha is currently managing the speeds of 4 late incoming flights. Flights 1 to 4, which were originally scheduled to arrive at the hub at the same time (assume that all 4 flights can land together because the hub has multiple runways). All of the passengers on these flights will change planes at the hub and then depart on four outgoing flights (Flights 5-8). The file Flight. xlsx contains the number of passengers on the four incoming flights and the number of those passengers who will be transferring to the four outgoing flights. For example, Flight 3 has 130 passengers who transfer to outgoing flight 6. The file also shows the number of minutes the flights are currently late (18, 15, 8 and 6 minutes for Flights 1-4, respectively). There are no other incoming flights, and all flights have a sufficient number of seats to hold all passengers.

Alpha’s policy is to hold outgoing flights until all connecting passengers are aboard. Scheduled connection times at the hub would allow on-time departures of outgoing flights if all incoming flights were on-time, but connection times contain no extra time. Therefore, if a passenger’s incoming flight is delayed by a certain number of minutes, that passenger’s outgoing flight must be delayed by at least the same number of minutes. For example, if Flight 3 does not speed up and is late by 8 minutes, then Flight 6 must be delayed by at least 8 minutes (Flight 6 may be delayed longer than 8 minutes if other connecting flights are even later). Again, every outgoing flight will take off as soon as all connecting passengers are aboard. Here, Alpha measures its delay costs in terms of delays to passengers on outgoing flights because passengers care about when they arrive at their final destination; they do not really care if their arrival at the hub is delayed. Delay costs are $0.45/passenger/minute of outgoing flight delay. As in part (a), speeding up by x minutes costs $7.5x2 .b.1: By how much should Alpha speed up each incoming flight?