We optimize profit, but profit as a function of what?

Answer 1

You optimize profit as a function of the price.
"His lab has developed two software modeling tools to identify where to locate the power stations and the likely profits as a function of the price of natural gas and petroleum, along with other factors, such as the number of fuel cell-powered vehicles on the road."

Answer 2

Economic models of a firm typically assume that a firm's objective is maximimize its profit. The variables that a firm's profit depends on include the demand for the firm's output, the firm's production costs, and (in some models) the behavior of other firms in the industry.