[[Q]]

Solve the following system of inequalities graphically:

4x + 3y ≤ 60, y ≥ 2x, x ≥3, x, y ≥ 0

4x + 3y ≤ 60 … (1)

y ≥ 2x … (2)

x ≥ 3 … (3)

The graph of the lines, 4x + 3y = 60, y = 2x,and x = 3, are drawn in the figure below.

Inequality (1) represents the region below the line, 4x +3y = 60 (including the line 4x + 3y = 60).Inequality (2) represents the region above the line, y = 2x(including the line y = 2x). Inequality (3)represents the region on the right hand side of the line, x =3 (including the line x = 3).

Hence, the solution of the given system of linear inequalities isrepresented by the common shaded region including the points on therespective lines as follows.