Question

Minimise $Z=x+2y$
subject to $2x+y\ge 3,x+2y\ge 6,x,y\ge 0$

Answer 1

The feasible region determined by the constraints, $2x+y\ge 3,x+2y\ge 6,x\ge 0,y\ge 0$ is as shown.
The corner points of the feasible region are $A(6,0)$ and $B(0,3)$
The values of $Z$ at these corner points are as follows.

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

It can be seen that the value of $Z$ at points $A$ and $B$ is same. If we take any other point such as $(2,2)$ on line $x+2y=6$, then $Z=6$
Thus, the minimum value of $Z$ occurs for more than $2$ points, and is equal to $6$