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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

illustration of tableau and pivot row

through the Gaussian process this tableau is generated

tableau after pivoting

What is the reasoning behind using Gaussian Elimination? Why does it generate a new and a better solution (a better z value)? Thank you.

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Just take a look here https://github.com/alvarogatenorio/Investigacion-Operativa

The link contains a pdf of operations research notes that I'm writing right now. The first section of chapter 2 contains all you need. However, if you are not familiar with the simplex theoretical foundations you will need to read the first chapter as well.

Unfortunatelly, everything is written in spanish, but I think is pretty understandable with a little help of google translate.

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