Answer
The answer is
At $(0,0)=0$
At $(0,8)=400$
At $(4,9)=610$
At $(8,0)=320$
Maximum value $=610$.
Minimum value $=0$.
Work Step by Step
The given objective function is $z=40x+50y$.
The value of the function at each corner points of the graph is shown below.
At $(0,0)$ is
$z=40(0)+50(0)$
$z=0+0$
$z=0$.
At $(0,8)$ is
$z=40(0)+50(8)$
$z=0+400$
$z=400$.
At $(4,9)$ is
$z=40(4)+50(9)$
$z=160+450$
$z=610$.
At $(8,0)$ is
$z=40(8)+50(0)$
$z=320+0$
$z=320$.
The maximum value of the objective function is $610$.
The minimum value of the objective function is $0$.
