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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.

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  • $\begingroup$ A numerical example might be helpful to answer your question. There are multiple related questions which are linked on the right side of this page. $\endgroup$ Commented Apr 8, 2019 at 16:16
  • $\begingroup$ After $254$ ($\textbf{ !}$) questions you should be able to make a table. Here you can find the code. $\endgroup$ Commented Apr 8, 2019 at 16:28
  • $\begingroup$ Your code has helped. Is my edited question OK now? $\endgroup$
    – user122424
    Commented Apr 8, 2019 at 16:43
  • $\begingroup$ 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. $\endgroup$ Commented Apr 8, 2019 at 16:50
  • $\begingroup$ 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. $\endgroup$
    – user122424
    Commented Apr 8, 2019 at 17:08

1 Answer 1

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In a problem that you use dual simplex to solve it, if you have a negative RHS and all the elements in that row are non-negative, then your original problem is infeasible and your dual problem is unbounded.

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