Answer
The answer is
At $(0,0)=0$
At $(0,9)=405$
At $(4,4)=300$
At $(3,0)=90$
Maximum value $405$.
Minimum value $0$.
Work Step by Step
The given objective function is $z=30x+45y$.
The value of the function at each corner points of the graph is shown below.
At $(0,0)$ is
$z=30(0)+45(0)$
$z=0+0$
$z=0$.
At $(0,9)$ is
$z=30(0)+45(9)$
$z=0+405$
$z=405$.
At $(4,4)$ is
$z=30(4)+45(4)$
$z=120+180$
$z=300$.
At $(3,0)$ is
$z=30(3)+45(0)$
$z=90+0$
$z=90$.
The maximum value of the objective function is $405$.
The minimum value of the objective function is $0$.
