Question

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

Answer 1

As clear from the graph, corner points are O,A,E, and D with coordinates (0,0), (52, 0), (144,16) and (0,38), respectivley. Also, given region is bounded.

Here, Z=3x+4y
$\because 2x+y=104$ and 2xy+4y =152
$\Rightarrow -3y=-48$
$\Rightarrow y=16$ and x=44
$\begin{array}{cc}\text{Corner points}& \text{Corresponding value of Z}\\ (0,0)& 0\\ (52,0)& 156\\ (44,16)& 196\leftarrow \text{Maximum}\\ (0,38)& 152\end{array}$
Hence, Z is at (44,16) is maximum and its maximum value is 196.