#### Answer

a. see graph
b. $z(0,0)=2(0)+3(0)=0$, $z(0,4)=2(0)+3(4)=12$, $z(3,2)=2(3)+3(2)=12$, $z(4,0)=2(4)+3(0)=8$
c. $12$, occurs on line segment from $(0,4)$ to $(3,2)$.

#### Work Step by Step

a. We can graph the system of inequalities representing the constraints as shown in the figure where the solution region is a four-side area in the first quadrant.
b. With the corner points indicated in the figure, we can find the values of the objective function as
$z(0,0)=2(0)+3(0)=0$, $z(0,4)=2(0)+3(4)=12$, $z(3,2)=2(3)+3(2)=12$, $z(4,0)=2(4)+3(0)=8$,
c. We can determine the maximum value of the objective function as $12$, which occurs on line segment from $(0,4)$ to $(3,2)$.