Use simplex method to solve the following problem. Maximize z $=$ x$1$ x$2+2$x$3$ Subject to $2$x$1+2$x$2+2$x$3<=6-$x$2+2$x$3<=4$ x$1,$ x$2,$ x$3>=0$ What is the optimal objective function value $($z value$)$ of the dual problem for the given problem?