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There are examples of linear programming (LP) problems where both the primal and dual problems are infeasible. For example, \begin{equation} \begin{aligned} &\min_x && x \\ &\ \ \text{s.t.} &&0\cdot x\leq -1 \end{aligned} \end{equation} On the other hand, there are examples of linear programming problems where the primal is infeasible and the dual is unbounded. For example, \begin{equation} \begin{aligned} &\min_x && x \\ &\ \ \text{s.t.} && x\geq 1 \\ & && x\leq 0 \\ \end{aligned} \end{equation} I am wondering: is there any geometric interpretation of this phenomenon? Is there some geometric difference between those infeasible LPs with infeasible duals and those infeasible LPs with unbounded duals?

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