# Solve the given inequalities x + 2y ≤ 100, 2x + y ≤ 120, x + y ≤ 70, x ≥ 0, y ≥ 0graphically in two – dimensional plane.

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Solve the given inequalities x + 2y ≤ 100, 2x + y ≤ 120, x + y ≤ 70, x ≥ 0, y ≥ 0graphically in two – dimensional plane.

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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, 