Solve the linear programming problem.

Minimize and maximize

$z=40x10y$

Subject to

$2xy48$

$xy32$

$x2y40$

$x,y0$

Select the correct choice below and fill in any answer boxes present in your choice. What is the minimum value of $z?$

A$.z=$

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

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