Answer
a. See graph
b. $z(0,2)= 4$, $z(0,4)= 8$, $z(2.4,2.4)= 14.4$, $z(4,0)= 16$, $z(2,0)= 8$
c. maximum $ 16$ at $(4,0)$.
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 pentagon shaped area in the first quadrant.
b. With the corner points indicated in the figure, we can find the values of the objective function as
$z(0,2)=4(0)+2(2)=4$, $z(0,4)=4(0)+2(4)=8$, $z(2.4,2.4)=4(2.4)+2(2.4)=14.4$, $z(4,0)=4(4)+2(0)=16$, $z(2,0)=4(2)+2(0)=8$,
c. We can determine that the maximum value of the objective function is $z(4,0)=16$, which occurs at $(4,0)$.
