#### Answer

a. See graph
b. $z(1,2)= -1$, $z(1,4) =-5$, $z(5,8)= -1$, $z(5,2)= 11$,
c. maximum $z(5,2)= 11$, occurs at $(5,2)$.

#### 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-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
$z(1,2)=3(1)-2(2)=-1$, $z(1,4)=3(1)-2(4)=-5$, $z(5,8)=3(5)-2(8)=-1$, $z(5,2)=3(5)-2(2)=11$,
c. We can determine that the maximum value of the objective function is $z(5,2)= 11$, which occurs at $(5,2)$.