Question

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

Answer 1

From the shaded bounded region, it is clear that the coordinates of corner points are $(\frac{3}{13},\frac{24}{13}),(\frac{18}{7},\frac{2}{7}),(\frac{7}{2},\frac{3}{4})and(\frac{3}{2},\frac{15}{4})$
Also, we have to determine maximum and minimum value of Z =x + 2y.
$\begin{array}{cc}\text{Corner points}& \text{Corresponding value of Z}\\ (\frac{3}{13},\frac{24}{13})& \frac{3}{13}+\frac{48}{13}=\frac{51}{13}=3\frac{12}{13}\\ (\frac{18}{7},\frac{2}{7})& \frac{18}{7}+\frac{4}{7}=\frac{22}{7}=3\frac{1}{7}Minimum\\ (\frac{7}{2},\frac{3}{4})& \frac{7}{2}+\frac{6}{4}=\frac{20}{4}=5\\ (\frac{3}{2},\frac{15}{4})& \frac{3}{2}+\frac{30}{4}=\frac{36}{4}=9Maximum\end{array}$
Hence, the maximum and minimum values of Z are 9 and $3\frac{1}{7}$, respectively.