Determine the maximum value of $Z = 3x + 4y$, if the feasible region (shaded) for a LPP is shown in following figure.

As clear from the graph, corner points are O, A, E and D with coordinates (0,0),(52,0),

(144,16) and (0,38), respectively. Also, given region is bounded.

Here $Z = 3x + 4y$

$2x + y = 104$ and $2x + 4y = 152$

$\Rightarrow$ $- 3y = - 48$

$\Rightarrow$ $y = 16$ and $x = 44$

Hence, Z is at (44,16) is maximum and its maximum value is 196 .