If evey linear program can be transformed to an unconstrained problem, then the optimum is unbounded because the objective is linear?

Question

Since optimization problems with linear equality constraints can be converted into an unconstrained problem this should apply for linear programs in standard form, right?

But doesn't this mean that the optimum is unbounded for every LP in standard form, since the objective is linear and the dual is infeasible?

Answer 1

No, because the "unconstrained" LP is actually constrained. At least some variables are $\geq0$.