### Duality in LP problem

##### All linear programming problems have another problem associated with them, which is known as its dual. In other words, every minimization problem is associated with a maximization problem and vice-versa. The original linear programming problem is known as primal problem, and the derived problem is known as its dual problem. The optimal solutions for the primal and dual problems are equivalent.

Conversion of primal to dual is done because of many reasons. The dual form of the problem, in many cases, is simple and can be solved with ease. Moreover, the variables of the dual problem contain information useful to management for analysis.

**Procedure**

##### Procedure is as follows:

Step 1: Convert the objective function if maximization in the primal into minimization in the dual and vice versa. Write the equation considering the transpose of RHS of the constraints.

Step 2: The number of variables in the primal will be the number of constraints in the dual and vice versa.

Step 3: The co-efficient in the objective function of the primal will be the RHS constraints in the dual and vice versa.

Step 4: In forming the constraints for the dual, consider the transpose of the body matrix of the primal problems.

__Sensitivity Analysis__

__Sensitivity Analysis__