Well its rather simple (I assume).
A commercial computer system for a leisure centre could be a very simple server with a few cleaver-terminals.
To complete tasks such as:
Tracking and predicting the costs, revenue and profit
A register system, to track how many members are in the leisure centre
The system could be connected to CCTV/ the centre's security
If you give it enough time you could think or many things a computer system in a commercial leisure centre could do.
Alevel Computing and IT student.