Answer
a. See graph
b. $z(0,2)= -4$, $z(0,3)= -6$, $z(5,3)= 19$, $z(5,0)= 25$, $z(2,0)= 10$
c. maximum $ 25$ at $(5,0)$.
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
$z(0,2)=5(0)-2(2)=-4$, $z(0,3)=5(0)-2(3)=-6$, $z(5,3)=5(5)-2(3)=19$, $z(5,0)=5(5)-2(0)=25$, $z(2,0)=5(2)-2(0)=10$,
c. We can determine that the maximum value of the objective function is $z(5,0)=25$, which occurs at $(5,0)$.
