Formulation of optimization technique in mathematical model?

Answer 1

The answer depends on the nature of the problem. In relatively simple cases, the solution may lie in constrained differentiation. A whole branch of mathematics - linear programming - deals with such questions where the objective to be optimised as well as the constraints within which the solution is required are all linear equations. Finally, there are numerical methods for dealing with miscellaneous optimisation problems.

With the limited amount of information given in the question, that is probably the best answer that can be given.