Past exam of the Probability, statistics and options II course of the University of Oxford / 2010 / T / T2 / b / i / Solution

Write $Ax=b$ as $Ax\le b$ and $-Ax\le -b$. The dual has nonnegative multipliers $u,v$ for these inequalities, with objective $b^{T}u-b^{T}v$ and condition $A^T(u-v)\ge c$. Every real vector $y$ can be expressed as $u-v$ with $u,v\ge 0$. HenceThe equality constraints remove the sign restriction on the dual variables.