Hi,

I was wondering if anyone could share some insights in how to solve this kind of problem:

Airline with overbooking plane.
Sells 120 tickets but only seats 100.
Ticket price = $200 non-refundable.
Cost x flying passenger = $80.
Overbooked cost per person who does not flight = $300.

If its equally likely that between 91-120 people will show up for the flight, how much expected profit, on the average will the airline generate?

How would you compute it? as a normal distribution? My guess in a simple way was:

from 91 to 99:
(120 tickets * Price Ticket) - (flying passengers * Cost of Flying passenger)

for 100
Same formula equals 16000

for 101 to 120
(120 tickets * Price Ticket) - (flying passengers * Cost of Flying passenger) - (passengers - 100)*overbooked cost

If you average the totals, it turns out 14020.


Any insight is appreciated,

Thanks