Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics IV / 5 / a / ii

For feasible solutions $\mathbf{x},\mathbf{y}$, nonnegativity givesThe first inequality uses $A^T\mathbf{y}\ge \mathbf{c}$ and $\mathbf{x}\ge 0$; the second uses $A\mathbf{x}\le \mathbf{b}$ and $\mathbf{y}\ge 0$. This is weak duality.