The objective function of a Linear Programming Problem (L.P.P.) is a function that needs to be optimized. It represents the goal or objective we want to achieve through the optimization process.

In a linear programming problem, we have a set of decision variables and a set of constraints. The decision variables represent the quantities or values we want to determine, while the constraints represent the limitations or restrictions on these variables. The objective function combines these decision variables in a way that reflects the desired outcome of the problem.

Let's consider an example to understand this better. Suppose we have a company that produces two products, A and B. The company wants to determine the optimal production quantities of these products to maximize their profit. The decision variables in this case would be the quantities of product A and product B produced.

The objective function would then be a function of these decision variables that represents the total profit generated by producing certain quantities of products A and B. It would be something like:

Objective function: Maximize Profit = 5A + 3B

In this example, the objective function is a linear function of the decision variables A and B, with coefficients 5 and 3 respectively. The objective is to maximize the value of this function, which represents the total profit.

The objective function can take different forms depending on the specific problem and the objective we want to achieve. It could be a minimization function, a maximization function, or even a combination of both. The coefficients of the decision variables in the objective function determine how much each variable contributes to the objective.

In summary, the objective function of a linear programming problem is a function that needs to be optimized. It represents the goal or objective we want to achieve through the optimization process. It is a function of the decision variables and reflects the desired outcome of the problem.