Answer
a. See graph
b. $z(0,10)= 60$, $z(10,0)= 50$, $z(\frac{10}{3},\frac{10}{3})= \frac{110}{3}\approx36.7$
c. maximum $ 60$ at $(0,10)$.
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 triangular area in the first quadrant.
b. With the corner points indicated in the figure, we can find the values of the objective function as
$z(0,10)=5(0)+6(10)=60$, $z(10,0)=5(10)+6(0)=50$, $z(\frac{10}{3},\frac{10}{3})=5(\frac{10}{3})+6(\frac{10}{3})=\frac{110}{3}\approx36.7$,
c. We can determine that the maximum value of the objective function is $z(0,10)=60$, which occurs at $(0,10)$.
