I'm sure Cyrano understands Yield Management, but trying to describe it in six paragraphs is like trying to describe how to fly an aircraft to PPL level in six paragraphs. For major carriers there is a whole department at HQ constantly managing and monitoring this. And they can't just pick up a £50 App to run the logic.
You need to know your market better than just "first 20 ...... next 20 ......". If you expect to get maybe the last 6 who book the day before going to business meetings, you need to make sure that they pay the higher fare, regardless of how many have booked earlier, so there's a lot of skill in what you offer, and when. If you manage to get corporate agreements with regular users giving them an x% discount, you maybe need to pitch even higher so after the discount you still are getting the amount you first thought of.
And finally: you make the entirely wrong assumption that a full or nearly-full flight means a profitable flight.
This one is oft-repeated. However, if a near-full flight is still not profitable it does show a real cock-up with the yield management.