# Solve the given inequalities x + 2y ≤ 2000, x + y ≤ 1500, y ≤ 600, x ≥ 0, y ≥ 0graphically in two – dimensional plane.

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Solve the given inequalities x + 2y ≤ 2000, x + y ≤ 1500, y ≤ 600, x ≥ 0, y ≥ 0graphically in two – dimensional plane.

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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,