The graphical representation of 5x + 4y ≤ 20, x ≥ 1, y ≥ 2 is given by common region in the figure below.

5x + 4y ≤ 20 ...... (1)

x ≥ 1 ...... (2)

y ≥ 2 ...... (3)

Inequality (1) represents the region below line 5x + 4y = 20 (**including the line** 5x + 4y = 20).

Inequality (2) represents the region in front of line x = 1 (**including the line** x = 1).

Inequality (3) represents the region above line y = 2 (**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,