Question

Maximise $Z=-x+2y$, subject to the constraints:
$x\ge 3,x+y\ge 5,x+2y\ge 6,y\ge 0$

Answer 1

The feasible region determined by the constraints, $x\ge 3,x+y\ge 5,x+2y\ge 6,y\ge 0$ is as shown.
It can be seen that the feasible region is unbounded.
The values of $Z$ at corner points $A(6,0),B(4,1)$ and $C(3,2)$ are as follows

Corner point	$Z=-x+2y$
$A(6,0)$	$Z=-6$
$B(4,1)$	$Z=-2$
$C(3,2)$	$Z=1$

As the feasible region is unbounded, therefore $Z=1$ may or may not be the maximum value
For this, we graph the inequality $-x+2y>1$ and check whether the resulting half plane has points in common with the feasible region or not
The resulting feasible region has points in common with the feasible region.
Therefore $Z=1$ is not maximum value. $Z$ has no maximum value.