How does the cost and revenue flow to the Profit Center?

The profit center is stored in the cost center this way the costs flow to the
profit center.

The profit center is also stored in material master. This way all sales
orders created for the finished product automatically picks up the profit
center from the material master and all the revenues and costs coming
from this sales order for that finished product is passed on to this profit
center.

A profit center document is created in addition to the Finance document
whenever revenue or consumption takes place. This document contains
the details of the profit center.

Once both the costs and revenues flow to the profit center you can write
reports using the Report Painter to get intelligent analysis. You can also
use SAP standard reports