Trading in the presence of priorities
If I understand you correctly, all customers prefer economy class to business class (that is, they only care about the lower price).

First, the way you've specified the problem, the airline will always make every seat a business class seat, because if no economy seats are available, the airline will (a) sell the same number of tickets (since customers buy business class if economy isn't available) and (b) sell all the tickets at a higher price.

But maybe you meant something like, fewer people will buy business class seats because the price is higher, so the airline may wish to make some seats economy class so they fill every seat. That is, the airline may initially wish to offer tickets for business class, wait until they stop getting new orders, then lower the price to economy class in order to fill the rest of the seats. Depending on the underlying model of demand and purchasing you may get different results.

I'll highlight one, the 'Coase conjecture', which argues that the sort of pricing scheme I described above will break down because customers rationally anticipate that the airline will lower prices as soon as they stop getting new orders, so they wait for the price to drop.