Past exam of the Probability, statistics and options II course of the University of Oxford / 2009 / T / T2 / b / i

Write each unrestricted coordinate as $x_j=u_j-v_j$ with $u_j,v_j\ge 0$. Then the primal has nonnegative variables $(u,v)$, constraint matrix $[A,-A]$, and objective coefficients $(c,-c)$. Its dual constraints are $A^{T}y\ge c$ and $-A^{T}y\ge -c$, hence equality. ThereforeThe removed sign restriction on the primal variables becomes equality of the dual column constraints.