Objective Function in Linear Programming

Linear Programming is a mathematical technique used to determine the best possible outcome or solution from a given set of constraints or limitations. The objective function is a key element in linear programming that defines the goal or objective of the problem.

Definition of Objective Function

The objective function is a mathematical expression that represents the quantity to be maximized or minimized in a linear programming problem. It is a linear combination of decision variables that are subject to constraints, and represents the ultimate goal that the decision maker wants to achieve.

Significance of Objective Function

The objective function is significant in linear programming because it helps to determine the optimal solution to the problem. The optimal solution is the one that maximizes or minimizes the objective function while satisfying all the constraints.

Types of Objective Functions

There are two types of objective functions in linear programming:

1. Maximization Objective Function: This type of objective function is used to maximize the value of the decision variables subject to constraints.

2. Minimization Objective Function: This type of objective function is used to minimize the value of the decision variables subject to constraints.

Conclusion

In conclusion, the objective function is a crucial component of linear programming as it defines the goal or objective of the problem. The objective function can either be a maximization or minimization function, and its value must be optimized subject to constraints in order to determine the optimal solution to the problem.