1. The problem statement, all variables and given/known data Weak Duality Theorem. If x ε ℝn is feasible for P and x ε ℝm is feasible for D, then cTx ≤ yTAx ≤ bTy. Thus, if P is unbounded, then D is necessarily infeasible, and if D is unbounded, then P is necessarily infeasible. Moreover, if cTx = bTy with x feasible for P and y feasible for D, then x must solve for P and y must solve for D. 2. Relevant equations c ε ℝn, b ε ℝm A ε ℝm x n P: maximize cTx subject to Ax ≤ b, 0 ≤ x, where the inequalities Ax ≤ b are to be interpreted componentwise. D: minimize bTy subject to ATy ≥ c, y ≥ 0. 3. The attempt at a solution So the "proof" that follows in my course notes starts with Then it basically gives a simple verification of the inequality and says that the other results obviously follow. I'm confused by the logic here. The theorem starts by choosing x and y feasible for P and D. Then it states that if P is unbounded, the inequality shows that there could be no feasible y ........................ which is strange because the inequality only works for a feasible x and y. Could someone clear this up for me?