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

Minimize

C $=$ x $3$y $+$ z

subject to

x $2$y $+3$z $<=30$

$2$x $+$ y $2$z $<=45$

$2$x $+$ y $+3$z $<=60$

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

The minimum is C $=$

at

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

$.$