If we have the following, $$ \text{max: } z = c^Tv $$ $$ \text{s.t } Av = u $$ $$ v \geq 0 $$ If this is unbounded, then can I state that for any vector $u'$ other than $u$ it will either be unbounded or infeasible
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1The Lagrange dual of your problem consists in maximizing the linear function $-u^\intercal, x$ subject to $A^\intercal x + c \ge 0$. Now, if $u$ varies, the admissible set is fixed and only the objective functions changes. It could help for finding a counterargument. – Smilia Apr 11 '21 at 08:14