Question

Maximise $Z=3x+4y$
Subject to the constraints :
$x+y\le 4,x\ge 0,y\ge 0.$

Answer 1

The feasible region determined by the constraints, $x+y\le 4,x\ge 0,y\ge 0.$ is as follows.


From the above graph the corner points of the feasible region are $(0,0),(4,0)$ and $(0,4)$.
The values of $Z$ at these points are as follows:

Corner points	$Z=3x+4y$
$(0,0)$	$0$
$(4,0)$	$12$
$(0,4)$	$16\to \text{Maximum}$

$\therefore$ The maximum value of $Z$ is $16$ at the point $(0,4)$.