This question is related to this TED video which shows a particularly interesting calculation of bumping passengers from a overbooked flight. The actual segment of that video is here.
The whole problem goes as follows: If there are 180 seats in an airplane what is the optimal number of tickets that the airline can sell that will yield the maximum revenue.
Now lets say each ticket costs 250 dollars and every bumped passenger must be paid 800 dollars as compensation. What is the optimal number of tickets the airline can sell ?
Now they offer a sample calculation of the expected returns for selling a 195 tickets. It is this calculation I am unable to understand.
It says the calculation is done via:
Expected value of 195 tickets = p(181) * 1 * 800 + p(182) * 2 * 800 + ..so on
My first question is why multiply the probability value with the cost ? What does it even mean : 2 * 800 * p(182) ? What does it even mean ? This calculation makes absolutely no sense to me.
My second question, is that why would you add up all the probability and cost multiplications ? I mean how does adding those up give you the expected value for selling 195 tickets.
I have no idea how this calculation even makes sense.