The graphical representation of 3x + 2y ≤ 12, x ≤ 1, y \(\ge\)2 is given by common region in the figure below.
3x + 2y ≤ 12 ...... (1)
x ≤ 1 ...... (2)
y \(\ge\)2 ..... (3)
Inequality (1) represents the region below line 3x + 2y = 12 (including the line).
Inequality (2) represents the region behind line x = 1 (including the line x=1).
Inequality (3) represents the region above line (including the line y = 2).
Therefore, every point in the common shaded region including the points on the respective lines represents the solution for the given inequalities.
This can be represented as follows,