Thread: Airline Ticket Price Problem - 3 variables.

So my problem is this:

I have to determine the best pricing structure for a 'simulated airline'.
There are 3 types of ticket;
Business Class seats @ $160 each, Premium Economy Class seats @ $125 each, and Super Saver Class seats @ $75 each.
A MINimum of 10% of the seats must be Business Class;
A MINimum of 50% must be Premium Economy Class tickets;
A MAXimum of 20% can be Super Saver Class tickets.
Of the Business Class seats it is predicted that only 52% will be sold, 65% of the Premium Economy Class tickets will be sold, and 76% of the Super Saver Class tickets will sell.

So the question is this... if I only have 108 seats on the aircraft what will be the best breakdown of tickets to get the maximum return given the restrictions on seat type allocations, expected sale %'s and different ticket costs?

So far I have only managed to work out an Excel based solution, using trial and error to work out the best results... but there must be a mathematical way of doing/illustrating this.

Any help gratefully received.
Thanks from New Zealand!

first up, allocate the seats you have no choice about:
at least 10.8 (round up to 11) seats must be business
at least 54 seats must be premium
at 21.6 (round up to 22) must be super saver

So we have allocated 11 + 54 + 22 = 87 seats so far.

How to allocate the remaining 21 seats
The expected revenue from an extra business seat is 52% * 160 = $83.20
The expected revenue from an extra premium seat is 65% * 125 = $81.25
The expected revenue from an extra super saver seat is 76% * 75 = $57.00

So, assuming you want to maximise expected revenue, how do you think the remaining seats should be allocated?