If the primal problem is constrained by equations instead of inequalities---Minimize cx subject to Ax=b and x≥0---then the requirement y≥0 is left out of the dual: Maximize yb subject to yA≤c. Show that the one-sided inequality yb≤cx still holds. Why was y≥0 needed in equation (1) but not here? This weak duality can be completed to full duality.