Answer
a. See graph
b. $z(0,0)=(0)+6(0)=0$, $z(0,5)=(0)+6(5)=30$, $z(2,6)=(2)+6(6)=38$, $z(5,0)=(5)+6(0)=5$
c. maximum $z(2,6)= 38$, occurs at $(2,6)$.
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
$z(0,0)=(0)+6(0)=0$, $z(0,5)=(0)+6(5)=30$, $z(2,6)=(2)+6(6)=38$, $z(5,0)=(5)+6(0)=5$,
c. We can determine that the maximum value of the objective function is $z(2,6)= 38$, which occurs at $(2,6)$.
