The graphical representation of 3x + y ≥ 12, x + y ≥ 9, x ≥ 0, y ≥ 0 is given by common region in the figure below.
3x + y ≥ 12 ........ (1)
x + y ≥ 9 ....... (2)
x ≥ 0 ......... (3)
y ≥ 0 ......... (4)
Inequality (1) represents the region above line 3x + y = 12(including the line 3x + y = 12).
Inequality (2) represents the region above line x + y = 9(including the line x + y = 9).
Inequality (3) represents the region in front of line x = 0 (including the line x = 0).
Inequality (4) represents the region above line y = 0 (including the line y = 0)
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,
