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As the title says, I'm wondering whether the terms LP primal and LP dual usually refers to any primal/dual pair of an LP (feasible or not), or just the optimal primal/dual pair.

The reason that I'm asking is that I found the following question (without context) in a review sheet: If an LP primal is infeasible, what can you say about its LP dual?

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    $\begingroup$ It refers to the primal and dual pair of models. $\endgroup$ Jan 3 '15 at 16:33
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If the primal problem is infeasible, then the dual problem is infeasible or unbounded.

The different cases can be summarized in a table:

\begin{array}{|c|c|c|c|} \hline \texttt{primal/dual}& \texttt{infeasible} & \texttt{optimal} & \texttt{unbounded} \\ \hline \texttt{infeasible} & \color{blue}{\checkmark} & \color{red}{\times} & \color{blue}{\checkmark} \\ \hline \texttt{optimal} & \color{red}{\times} & \color{blue}{\checkmark} & \color{red}{\times} \\ \hline \texttt{unbounded} & \color{blue}{\checkmark} & \color{red}{\times} & \color{red}{\times} \\ \hline \end{array}

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