What is the purpose of an objective function in linear programming?

In linear programming, the objective function serves as the mathematical representation of the goal to be achieved, such as maximizing profit or minimizing costs. It is a single linear expression that quantifies the performance of a system based on the variables being manipulated.1234

The primary purpose of this function is to provide a clear criterion for identifying the "best" solution among all possible options. Because linear programming problems are subject to various constraints—such as limited resources, labor, or machine time—the feasible solutions are restricted to a specific region. The objective function allows researchers to evaluate different points within this feasible set to determine which one yields the optimal (largest or smallest) value.14235

By defining this goal in rigorous mathematical terms, analysts can use systematic procedures, such as the simplex method, to navigate the constraints and pinpoint the exact values for the variables that satisfy the objective.35