Thu September 26, 2013 By: Akanksha

How will we know whether the region is bounded or not?

Expert Reply
Vimala Ramamurthy
Thu September 26, 2013
Bounded feasible regions have both a minimum and a maximum value. Unbounded feasible regions have either a minimum or maximum value, never both.
Consider the following region:
x > 1

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

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