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Solve the given inequalities 4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x ≥ 0, y ≥ 0graphically in two – dimensional plane.

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The graphical representation of 4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x ≥ 0, y ≥ 0 is given by common region in the figure below. 

4x + 3y ≤ 60.…… (1) 

y ≥ 2x……. (2) 

x ≥ 0 ……. (3) 

y ≥ 0 ……. (4) 

x ≥ 3 ……. (5) 

Inequality (1) represents the region below line 4x + 3y = 60 (including the line 4x + 3y = 60 ).

Inequality (2) represents the region above line y = 2x (including the line y = 2x ). 

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 in front of line x = 3 (including the line x = 3) 

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,

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