Solve the linear programming problem.

Maximize $z=15x+15y$

subject $to7x+6y$

$,14x-12y$

$,x+42$

$,x+42$

$,x$

$,0$

$,0$

What is the maximum value of z$?$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.z=$

$($Type an integer or a fraction.$)$

B$.$ There is no maximum value of $z.$

At what corner point$($s$)$ does the maximum value of $z$ occur? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The maximum value of $z$ occurs only at the point$($s$)$

$($Type an ordered pair. Use a comma to separate answers as needed.$)$

B$.$ The maximum value of $z$ occurs at the points $$ and at all points connecting them.

$($Type an ordered pair. Use a comma to separate answers as needed.$)$

C$.$ There is no maximum value of z $.$