Question

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.

QUESTION:

The airline hires a marketing consultant. The marketing consultant suggests 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 (try to ignore the fact that this implies at some point no one will be left in New York!). 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?

Answer 1

Under new scheme cost would be:

C(C-NY )= 3*(50000+10*240)+50000+10*0

C (C-NY )= 200,000+7200

C (C-NY )= 207200

C(NY-C)= 4*(50000+10*240)

C(NY-C)= 200000+9600

Total Cost = C (C-NY +C(NY-C)

TC(Under new Scheme)= 207200+209600 = 416800

Cost under current system:

C(C-NY )= 2*(50000+10*240) +2*(50000+10*120)

C(C-NY )= 200,000+7200

C(C-NY )=207,200

C(NY-C)= 4*(50000+10*240)

C(NY-C)= 200000+9600

C(NY-C)=209600

Total cost = 207200+209600

TC(Current Scheme)=416800

Since the total cost to and from ChiCago To New York are equal. The two system are equally good.