Question

Maximise $Z=3x+2y$
subject to $x+2y\le 10,3x+y\le 15,x,y\ge 0$

Answer 1

The feasible region determined by the constraints $x+2y\le 10,3x+y\le 15,x,y\ge 0$ is as shown.
The corner points of the feasible region are $A(5,0),B(4,3)$ and $C(0,5)$.
The values of $Z$ at these corner points are as follows.

Corner points	$Z=3x+2y$
$A(5,0)$	$15$
$B(4,3)$	$18$	$\to$ Maximum
$C(0,5)$	$10$

Therefore, the maximum value of $Z$ is $18$ at the point $(4,3)$