Operation Research 6: Linear Programming Solution: Simplex Method for Minimization

Linear Programming Solution using Simplex Method for Minimization objective function.
The steps to solve minimization linear programming problem using simplex method:
1- Convert each inequality in the set of constraints to an equality by adding slack variables.
2- Create the initial simplex tableau.
3- Locate the most negative entry (Cj-Zj) in the bottom row to determine the pivot column.
4- The smallest positive ratios of “RHS-column” with their corresponding pivot column is pivot row.
5- Use elementary row operations so that the pivot value is 1, and all other entries in the entering column are 0. This process is called pivoting.
6- If all (Cj-Zj) ≥ 0, this is the final table. If not, go back to Step 3 to determine the pivot column again.
7- From the final table, the LPP has a minimum solution, which is given by the entry in the lower-right corner of the table.