Answer
a. See graph
b. $z(0,4)= 8$, $z(0,8)= 16$, $z(4,0)= 12$,
c. Maximum $ 16$, at $(0,8)$.
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 triangle in the first quadrant.
b. With the corner points indicated in the figure, we can find the values of the objective function as
$z(0,4)=3(0)+2(4)=8$, $z(0,8)=3(0)+2(8)=16$, $z(4,0)=3(4)+2(0)=12$,
c. We can determine the maximum value of the objective function as $z(0,8)= 16$, which occurs at $(0,8)$.
