Show directly that if the primal problem Minimize cx subject to Ax ≥ b and x ≥0 has no feasible solutions, and if the dual problem has feasible solution, then dual problem is unbounded.

Use Farkas’ lemma. If the system Ax ≥ b and x ≥ 0 has no solutions, then system wA ≤ 0, w ≥ 0, wb > 0 has solution.