#### Answer

$z(0,0)= 0$, $z(0,9)= 405$, $z(4,4)= 300$, $z(3,0)= 90$
maximum $z(0,9)= 405$
minimum $z(0,0)= 0$

#### Work Step by Step

Step 1. Given the objective function $z(x,y)=30x+45y$, we can obtain the function values at each corner as
$z(0,0)=30(0)+45(0)=0$
$z(0,9)=30(0)+45(9)=405$
$z(4,4)=30(4)+45(4)=300$, $z(3,0)=30(3)+45(0)=90$
Step 2. We can find the maximum of $z$ as $z(0,9)= 405$
Step 3. We can find the minimum of $z$ as $z(0,0)= 0$