The shaded area in the given figure is a solution set for some system of inequations. The maximum value of…
The shaded area in the given figure is a solution set for some system of inequations. The maximum value of the function $z=10 x+25 y$ subject to the linear constraints given by the system is
80
100
95
105
Solution
$\begin{aligned} & \text { At }(0,0), z=10(0)+25(0)=0 \\ & \text { At }(3,0), z=10(3)+25(0)=30 \\ & \text { At }(3,2), z=10(3)+25(2)=80 \\ & \text { At }(2,3), z=10(2)+25(3)=95 \\ & \text { At }(0,3), z=10(0)+25(3)=75\end{aligned}$
$\therefore \quad$ Maximum value of $\mathrm{z}$ is 95 .
