No compactness assumption is imposed on the feasible polyhedron. Linear objectives attain their finite optima on nonempty polyhedra even when those polyhedra are unbounded. This is the attainment step used with Farkas' lemma to obtain an optimal dual certificate. The supplied proof applies Farkas' lemma to the original system with an objective threshold equal to the finite supremum; a separating certificate would contradict feasibility or produce a strictly smaller dual upper bound.