Find the optimal solution for the following problem. $($Round your answers to $3$ decimal places.$)$

Minimize C $=12$x $+4$y $+11$z

subject to $7$x $+13$y $+20$z $>=67$

$14$x $+18$y $+6$z $>=134$

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

What is the optimal value of x$?$

What is the optimal value of y$?$

What is the optimal value of z$?$

What is the minimum value of the objective function?