Question

Solve the following Linear Programming Problem graphically:
Maximize $Z=3x+4y$
Subject to the constriants:
$x+y\le 4,x\ge 0,y\ge 0$

Answer 1

Maximize $Z=3x+4y$
Subject to
$x+y\le 4,x\ge 0,y\ge 0$
$x+y=4$

$\begin{array}{ccc}x& 0& 4\\ y& 4& 0\end{array}$
$\begin{array}{cc}\text{Corner points}& \text{Value of}Z=3x+4y\\ (0,4)& 16\\ (4,0)& 12\\ (0,0)& 0\end{array}$

Hence, $Z$ is maximum at $(0,4)$ and maximum value is $16$.