#### Answer

a. See graph
b. $z(0,3)= 3$, $z(0,4)= 4$, $z(3,0)= 12$, $z(6,0)= 24$
c. maximum$ 24$, occurs at $(6,0)$.

#### 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-sided area in the first quadrant.
b. With the corner points indicated in the figure, we can find the values of the objective function as
$z(0,3)=4(0)+(3)=3$, $z(0,4)=4(0)+(4)=4$, $z(3,0)=4(3)+(0)=12$, $z(6,0)=4(6)+(0)=24$,
c. We can determine that the maximum value of the objective function is $z(6,0)= 24$, which occurs at $(6,0)$.