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,