Inequalities are 3x + 2y ≤ 12, x ≥ 1, y ≥ 2 (i) The line l1 : 3x + 2y = 12 passes through (4, 0), (0, 6) AB represents the line, 3x + 2y = 12. Consider the inequality 3x + 2y ≤ 12 Putting x = 0, y = 0 in 3x + 2y ≤ 12 0 + 0 ≤ 12, which is true. Therefore, origin lies in the region 3x + 2y ≤ 12 ∴ The region lying below the line AB including all the points lying on it. (ii) The line l2 : x = 1 passes through (1, 0). This line is represented by EF. Consider the inequality x ≥ 1 Putting x = 0, 0 ≥ 1, which is not true. Therefore, origin does not lie in the region of x ≥ 1 The region lies on the right of EF and the points on EF from the inequality x ≥ 1. (iii) The line l3 : y = 2 passes through (0, 2). This line is represented by CD. Consider the inequality y ≥ 2 Putting y = 0 in y ≥ 2, we get 0 ≥ 2 which is false. ∴ Origin does not lie in the region of y ≥ 2 y ≥ 2 is represented by the region above CD and all the points on this line. Hence, the region satisfying the inequalities. 3x + 2y ≥ 12, x ≥ 1, y ≥ 2 is the ΔPQR.