Calculate the optimal solution of the linear programming model below using the bounded variables algorithm. $($It is a method used to solve linear programming problems where upper or lower limits limit some variables.$)($xB$,$ Li$,$ Lu$,,$cj$,$ theta, etc.$)$

max. z $=2$X$1+$ X$2+3$X$3$

s$.$t$.$

$4$X$1-$ X$2<=12$

$-$X$1+$ X$2+2$X$3<=10$

$-3$X$1+$ X$2+4$X$3<=12$

$1<=$ X$1<=3,0<=$ X$2<=5,1<=$ X$3<=4$