$15$ Points$)$ Take the dual of the following problem.

minimize Z $=4$x$12$x$2+3$x$3+$x$4$ x$1,$x$2,$x$3,$x$4$

$2$x$13$x$2+$x$3+5$x$4$x$12$x$3+3$x$42$x$1+$x$23$x$3$x$4$ x$1,$x$2$

x$1,$x$2,$x$3,$x$4,$x$5,$x$6,$x$7>=0.$

subject to:

$<=5,=1,$

$>=3,$

$>=0,$x$3<=0,$x$4$free.