# Dual Simplex Method

Suppose that in a Linear Programming problem in the dual Simplex Method there is a first element (in the first column) negative. If there are in that pivot row some negative numbers we take $$\max$$ from the first row and that pivot row. But what if all the elements in the pivot row are positive, what pivot do we use, i.e. which column? Consider this table $$\begin{array}{|c|c|c|c|c|c|c|c|}\hline -4& 0 & 1&5&16&0&4&0 \\ \hline -12& 0 & 8&-1&-7&0&-3&1 \\ \hline 1& 1 & 1&1&1&1&1&1 \\ \hline \end{array}$$ We take -3 in the second row. OTHER new initial TABLE: $$\begin{array}{|c|c|c|c|c|c|c|c|}\hline -4& 0 & 1&5&16&0&4&0 \\ \hline -12& 0 & 8&1&7&0&3&1 \\ \hline -1& 1 & 1&1&1&1&1&-1 \\ \hline \end{array}$$ What do we take here? Note that the first and last element in the last row have the opposite signs in compared with the previous table.

• After $254$ ($\textbf{ !}$) questions you should be able to make a table. Here you can find the code. Commented Apr 8, 2019 at 16:28
• Your code has helped. Is my edited question OK now? Commented Apr 8, 2019 at 16:43
• Great job (+1). Maybe it would be helpful if you provide the problem before you transformed into tables. At the moment I just think:"Have she/he made all the steps right before? And what was the original problem?" But this are my thoughts. Commented Apr 8, 2019 at 16:50
• May I suppose that I have these tables at the very beginning? I wanted to separate the first column and the first row by double line as here: = and || but I didn't succeeded. Commented Apr 8, 2019 at 17:08