In the simplex method, a tableau is created. An entering variable is generated and then using a criteria the exiting variable is also selected. This gives a pivot column and row and pivot element.
The next step in the basic simplex algorithm is to perform Gaussian Elimination. For example starting with this tableau
through the Gaussian process this tableau is generated
What is the reasoning behind using Gaussian Elimination? Why does it generate a new and a better solution (a better z value)? Thank you.