Matrix

What is Linear Programming?

Linear programming or Linear optimization is a technique that helps us to find the optimum solution for a given problem, an optimum solution is a solution that is the best possible outcome of a given particular problem.

In simple terms, it is the method to find out how to do something in the best possible way. With limited resources, you need to do the optimum utilization of resources and achieve the best possible result in a particular objective, such as the least cost, the highest margin, or the least time.

The situation that requires a search for the best values of the variables subject to certain constraints is where we use linear programming problems. These situations cannot be handled by the usual calculus and numerical techniques.

Linear Programming Definition

Linear programming is the technique used for optimizing a particular scenario. Using linear programming provides us with the best possible outcome in a given situation. It uses all the available resources in a manner such that they produce the optimum result.

Components of Linear Programming

The basic components of a linear programming(LP) problem are:

• Decision Variables:

  Variables you want to determine to achieve the optimal solution.

• Objective Function: An arithmetic

  equation that represents the goal you want to achieve

• Constraints:

  Limitations or restrictions that your decision variables must follow.

• Non-Negativity Restrictions:

  In some

  real-world scenarios, decision variables cannot be negative

Additional Characteristics of Linear Programming

• Finiteness:

  The number of decision variables and constraints in an LP problem is finite.

• Linearity:

  The objective function and all constraints must be linear functions of the decision variable

  It means the degree of variables should be one.