Answer
a. See graph
b. $z(0,0)= 0$, $z(0,6)= 72$, $z(3,4)= 78$, $z(5,0)= 50$,
c. maximum $ 78$ at $(3,4)$.
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
$z(0,0)=10(0)+12(0)=0$, $z(0,6)=10(0)+12(6)=72$, $z(3,4)=10(3)+12(4)=78$, $z(5,0)=10(5)+12(0)=50$,
c. We can determine that the maximum value of the objective function is $z(3,4)=78$, which occurs at $(3,4)$.
