Simplex Method - Simplified and Easiest way - 1- Basic Points

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Linear Programming

Simplex Method

Solving LPP with "Less than or equal to" types of constraints by Simplex Method.

You should take care about Simplex method only works with "≤" type inequality and independent coefficients higher or equal to zero, and you will have to standardize the restrictions for the algorithm.
The first step of the simplex method requires that we convert each inequality constraint in an LP formulation into an equation. Less-than-or-equal-to constraints (≤) can be converted to equations by adding slack variables, which represent the amount of an unused resource. To convert these inequality constraints to equalities, we add slack variables S1, S2,… to the left side of the inequality. Since slack variables represent unused resources (such as time on a machine or labor-hours available), they yield no profit. But we must add them to the objective function with zero profit coefficients.

The steps involved in using the simplex method to help solve an LP problem in which the objective function is to be maximized can be summarized as follows:

1) Choose the variable with the greatest positive Cj - Zj value to enter the solution.

2) Determine the row to be replaced by selecting the one with the smallest (non-negative) ratio of quantity to pivot column.

3) Calculate the new values for the pivot row.

4) Calculate the new values for the other row(s).

5) Calculate the Cj and Cj - Zj values for this tableau. If there are any Cj - Zj numbers greater than zero, return to step-1.

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