Solve the given inequalities 3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0graphically in two – dimensional plane.

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Solve the given inequalities 3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0graphically in two – dimensional plane.

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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,