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?
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}
