Use the technique developed in this section to solve the minimization problem.

Minimize C $=200$x $+150$y $+120$z

subject to $30$x $+15$y $+$ z $>=15$

x $+$ y $+2$z $>=30$

x $>=0,$ y $>=0,$ z $>=0$

The minimum is

C $=$

at

$($x$,$ y$,$ z$)=$

$.$