Maximize $,Z=x_1-3x_2+2x_3,$

subject to

$2x_1+2x_2-2x_{3}6,($ resource $1)$

$-x_2+2x_{3}4,($ resource $2)$

and

$x_{1}0,x_{2}0,x_{3}0.$

What is the optimal objective function value $(z$ value$)$ of the dual problem for the given problem?

$1$

$2$

$3$

$4$

None of the above