What is Objective Function?

As the name suggests, the objective function basically sets the objective of the Problem. It focuses on decision-making based on constraints. It is a real-valued function that is either to be maximized or minimized depending upon the constraints. It is like a Profit or a Loss function. It is usually denoted by Z. 

The terminologies associated with Objective Function are as follows:

• Constraints: They are basically the conditional equations that govern the Linear function
• Decision Variables: The variables whose values are to be found out. The equations are solved so as to get the optimal value of these variables.
• Feasible Region: It is the region in the graph where the constraints are satisfied and the decision variables are found at the corners of the region.
• Optimum Solution: The best possible solution that satisfies all constraints and achieves the highest or lowest objective.
• Infeasible Solution: A solution that violates one or more constraints and cannot be implemented or executed.

Objective Function in Linear Programming

In Linear Programming an objective function is a linear function comprising two decision variables. It is a linear function that is to be maximized or minimized depending upon the constraints. If a and b are constants and x and y are decision variables where x > 0 and y > 0, then the Objective function is

Z = ax + by

So in order to get the optimal value of the Optimization function first we need to solve the constraints using any of the techniques and find out the decision variables. Then we put the values of Decision variables in the Objective function to generate the optimal value.

Objective Function is the objective of the Linear Programming Problem as the name suggests. In linear programming or linear optimization, we use various techniques and methods to find the optimal solution to the linear problem with some constraints. The technique can also include inequality constraints as well. The objective function in Linear Programming is to optimize to find the optimum solution for a given problem.

In this article, we will learn all about the Objective Function including its definition, types, how to formulate an objective function for any given problem, etc. We will also learn various representations of Objective Functions such as Linear Objective Functions or Non-linear objective functions. So, let’s start learning about this fundamental concept in Linear Programming i.e., “Objective Function”.