Say I have a primal program P with n variables and c constraints. Let's say that I have an optimal solution for the dual program D, in which the y1, the variable related to the first constraint in P, is zero. Does that imply that I could run Simplex on P without the first constraint and get the same optimal solution as if ran Simplex with the first constraint?

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    $\begingroup$ Look up complementary slackness. $\endgroup$ – Yuval Filmus Feb 2 at 6:16

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