The graphical representation of x + 2y ≤ 2000, x + y ≤ 1500, y ≤ 600, x ≥ 0, y ≥ 0 is given by common region in the figure below.
x + 2y ≤ 2000 ............. (1)
x + y ≤ 1500 ........ (2)
y ≤ 600 ........ (3)
x ≥ 0 ........ (4)
y ≥ 0 .......... (5)
Inequality (1) represents the region below line x + 2y = 2000 (including the line x + 2y = 2000 ).
Inequality (2) represents the region below line x + y = 1500 (including the line x + y = 1500).
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 y = 600 (including the line y = 600)
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,