$3.$ Solve the following asymmetrical primal$-$dual linear program:

Primal

Min: Z$=2*$x$1+$x$2-$x$3$

Subject to:

x$1+$x$2-$x$3=1$

x$1-$x$2+$ x$3>=2$;

x$2+$x$3<=3$;

x$1>=0,$ x$2<=0$ and x$3$ is an unrestricted variable.

$($i$)$ Set$-$up the dual problem, $($ii$)$ Validate the weak duality theorem, and $($iii$)$

Validate the main duality theorem by using the complementary slackness theorem.