Linear Programming

Definition: The Linear Programming method is a technique of selecting the best alternative out of the available set of feasible alternatives, for which the objective function and the constraint function can be expressed as linear mathematical functions.

There are certain prerequisites for applying the linear programming technique. These are:

1. There should be an objective, clearly defined and measurable in quantitative terms. Such as, maximization of sales, minimization of cost of production, etc.
2. The activities included should be distinctively identifiable and measurable in quantitative terms. Such as products included in the problem of production planning.
3. The resources to be allocated for the attainment of the objective must be distinctively identifiable and measurable in quantitative terms. These resources must be in limited supply.
4. The objective function and the constraint function must be linear in nature.
5. The decision maker should have a series of feasible alternative course of actions, determined through resource constraints.

When these conditions are satisfied for a particular situation, the problem can be expressed in the algebraic form, called Linear programming problem. First of all, the linear programming problem is formulated and then it is solved for optimal decision.

How to formulate the Linear programming problem?

Once the prerequisite conditions for the formation of linear programming problem is satisfied, the firm decides on which objective is to be attained, such as maximization of profit or minimization of cost. This gives rise to two cases:

• Maximization case
• Minimization case.

The Linear programming is an important part of the mathematics field and is also called as “Optimization Techniques”. It is used in the day to day operations of each business and plays a vital role in the allocation of resources to different business operations.