Solve the given inequalities 3x + y ≥ 12, x + y ≥ 9, x ≥ 0, y ≥ 0. graphically in two – dimensional plane.
The graphical representation of 
is given by common region in the figure below.
.…… (1)
……. (2)
……. (3)
……. (4)
Inequality (1) represents the region above line 
(including the line 
).
Inequality (2) represents the region above line 
(including the line 
).
Inequality (3) represents the region in front of line 
(including the line 
).
Inequality (4) represents the region above line 
(including the line 
)
It is clear from the graph , that the region is unbounded.
Therefore , the following system of inequation is an unbounded set.
This can be represented as follows,
1