The graphical representation of x + 2y ≤ 100, 2x + y ≤ 120, x + y ≤ 70, x ≥ 0, y ≥ 0 is given by common region in the figure below.
x + 2y ≤ 100 ........ (1)
2x + y ≤ 120 ......... (2)
x ≥ 0 ........... (3)
y ≥ 0 ........ (4)
x + y ≤ 70 ......... (5)
Inequality (1) represents the region below line x + 2y = 100 (including the line x + 2y = 100).
Inequality (2) represents the region below line 2x + y = 120 (including the line 2x + y = 120).
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).
Inequality (5) represents the region below line x + y = 70 (including the line x + y = 70)
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,