Ive the linear programming problem.

Minimize and maximize

$z=10x20y$

Subject to

$3xy54$

$xy42$

$x3y48$

$x,y0$

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

A$.z=450$

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

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

Select the correct choice below and fill in any answer boxes present in your choice. What are the coordinates of the corner point where the minimum value of $z$ occurs?

A$.$ The coordinates are $$

$($Type an ordered pair.$)$

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