Question

Minimise and Maximise $Z=x+2y$
Subject to$x+2y\ge 100,2x-y\le 0,2x+y\le 200;x,y\ge 0$

Answer 1

Minimise and Maximise $Z=x+2y$
Subject to$x+2y\ge 100,2x-y\le 0,2x+y\le 200;x,y\ge 0$
$x+2y=100$
$\begin{array}{ccc}x& 0& 100\\ y& 50& 0\end{array}$

$2x-y=0$
$\begin{array}{ccc}x& 0& 50\\ y& 0& 100\end{array}$

$2x+y=200$
$\begin{array}{ccc}x& 100& 0\\ y& 0& 200\end{array}$

$\begin{array}{cc}\text{Corner Points}& \text{Value of}Z=x+2y\\ (0,200)& 400\\ (0,50)& 100\\ (20,40)& 100\\ (50,100)& 250\end{array}$
$\therefore Z=400$ is maximum at $(0,200$)

Also,
$Z$ is minimum at two points $(0,50)\text{and}(20,40)$
$\therefore Z=100$ is minimum at all points joining $(0,50)\text{and}(20,40)$.