Answer
$z(0,0)= 0$, $z(0,8)= 400$, $z(4,9)= 610$, $z(8,0)= 320$
maximum $z(4,9)= 610$
minimum $z(0,0)= 0$
Work Step by Step
Step 1. Given the objective function $z(x,y)=40x+50y$, we can obtain the function values at each corner as
$z(0,0)=40(0)+50(0)=0$,
$z(0,8)=40(0)+50(8)=400$,
$z(4,9)=40(4)+50(9)=610$,
$z(8,0)=40(8)+50(0)=320$,
Step 2. We can find the maximum of $z$ as
$z(4,9)=40(4)+50(9)=610$
Step 3. We can find the minimum of $z$ as
$z(0,0)=40(0)+50(0)=0$
