The graphical representation of 3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0 is given by common region in the figure below.
3x + 4y ≤ 60 ...... (1)
x + 3y ≤ 30 ..... (2)
x ≥ 0 ....... (3)
y ≥ 0 ...... (4)
Inequality (1) represents the region below line 3x + 4y = 60 (including the line 3x + 4y = 60).
Inequality (2) represents the region below line x + 3y = 30 (including the line x + 3y = 30).
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).
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,