$4\mathrm{.}6-9.*$ Consider the following problem.

Minimize Z # $3$x$1$ $ $2$x$2$ $ $4$x$3,$

subject to

$2$x$1$ $ x$2$ $ $3$x$3$ # $60$

$3$x$1$ $ $3$x$2$ $ $5$x$3\%120$

and

x$1\%0,$ x$2\%0,$ x$3\%0.$

$($b$)$ Using the two$-$phase method, work through the simplex

method step by step to solve the problem.