In following figure, the feasible region (shaded) for a LPP is shown. Determine the maximum and minimum value of $Z = x + 2y$.

From the shaded bounded region, it is clear that the coordinates of corner points are

$\left( {\frac{3}{{13}},\frac{{24}}{{13}}} \right),\left( {\frac{{18}}{7},\frac{2}{7}} \right),\left( {\frac{7}{2},\frac{3}{4}} \right)$

and $\left( {\frac{3}{2},\frac{{15}}{4}} \right)$.

Also, We have the following conditions as per the question, to determine maximum and minimum value of $Z = x + 2y$.

Hence, the maximum and minimum values of Z are 9 and $3\frac{1}{7}$, respectively.