I think your guess at gate receipts is about right, but in the FA cup the teams split the money of the home gate 45/45 with 10% going to the FA, which is why teams don't give away tickets with season tickets etc, as the other team wouldn't get a cut of that. Granted, I don't know if that happens in the League cup though.
Without knowing the player bonuses, police costs, etc, I can't figure it out, but I think we and any other team pulling in 10k crowds makes a loss.
We're ok with it, as our Prem money evens it out easily, but a team like Sheff Utd for example probably struggle, which is odd when you think about it.
It's another version of the Europa league actually being a pain in the backside for clubs, rather than a good thing.