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

Maximize C $=10$x $+6$y $+9$z

subject to $9$x $+11$y $+18$z $<=69$

$12$x $+14$y $+4$z $<=138$

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 maximum value of the objective function?