The inequalities are 5x + 4y ≤ 20, x ≥ 1, y ≥ 2 (i) The line $l_1$ : 5x + 4y = 20 passes through (4, 0) and (0, 5). This line is represented by AB. Consider the inequality 5x + 4y ≤ 20 Putting x = 0, y = 0 0 + 0 = 0 ≤ 20, which is true. The origin lies in this region, i.e., region below the line 5x + 4y = 20 and all the points lying on it belong to 5x + 4y ≤ 20. (ii) The line $l_2$ : y = 2, line is parallel to x-axis at a distance 2 from the origin. It is represented by EF. Putting y = 0, 0 ≥ 2 is not true. Origin does not lie in this region. Region above y = 2 represents the inequality y ≥ 2 including the points lying on it. (iii) The line l3 : x = 1, line parallel to y-axis at a distance 1 from the origin. It is represented by CD. Putting x = 0 in x – 1 ≥ 0 –1 ≥ 0, which is not true. Origin does not lie in this region. ∴ The region on the right of x = 1 and all the points lying on it belong to x ≥ 1. ∴ Shaded area bounded by ΔPQR is the solution of given inequalities.