The cost to United Airlines of flying a single plane from Chicago to New York is given by:
C=50,000+10q
where "q" is the number of passengers on the plane. Each plane holds up to 240 people. United flies this route 4 times per day (7am, 10am, 1pm and 4pm). The 7am and 4pm flights are always full, but the 10am and 1pm flights are only half full.
1) Calculate the average cost per passenger for the full flights and for the half full flights.
2) You suggest to United that they might want to fly only one flight in the middle of the day, so it would be full. United says this is crazy, however, since they fly all four of these planes back to Chicago from New York, and when they fly back they are full on all four trips. Assuming you need to fly all of these four flights back from New York, and would therefore need to fly one empty plane from Chicago under your new suggestion, calculate the cost per passenger for a day of flying under your new scheme versus the current system. Which is better?
3) How would your response to part (2) change if United told you that sometimes the 10am flight from Chicago is 3/4 full?
4) Now suppose cost function differed depending on whether there are any passengers on plane at all. Specifically, assume instead that it only costs 45000 to fly an empty plane from Chicago to New York because you now no longer need any cabin crew. This reduces fixed cost by 5000. How might this change answer to part (c)?