How will we know whether the region is bounded or not?
y > 0
2x + y < 6
The intersection of the above graphs are shaded in green as follows:
Since the region is finite, it is bounded and it is having both maximum and minimum value
Now consider the functiolns
2x + y > 3
3y - x < 9
2x + y < 10
The graph of the above system of inequalities are not finite and hence it is unbounded.
The maximum point occurs at (3, 4) but there is no minimum value and hence the region is unbounded