Provide a stepwise synthesis to carry out the following conversion. 
Definitions:
Production Function
A production function is a mathematical model that describes the relationship between inputs used in production (like labor and capital) and the output produced.
Profit
The financial gain achieved when the revenues obtained from business activities exceed the expenses, costs, and taxes associated with maintaining the activity.
Commodity
A primary item used in trading that is replaceable with other items of the same type.
Maximise
To increase to the greatest possible amount or degree.
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