Answer
a. See graph
b. $z(0,3)= 12$, $z(0,9)= 36$, $z(9,0)= 18$, $z(6,0)= 12$, $z(1.5,1.5)= 9$
c. maximum $ 36$ at $(0,9)$.
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
$z(0,3)=2(0)+4(3)=12$, $z(0,9)=2(0)+4(9)=36$, $z(9,0)=2(9)+4(0)=18$, $z(6,0)=2(6)+4(0)=12$, $z(1.5,1.5)=2(1.5)+4(1.5)=9$,
c. We can determine that the maximum value of the objective function is $z(0,9)=36$, which occurs at $(0,9)$.
