The inequalities are 3x + 2y ≤ 150, x + 4y ≤ 80, x ≤ 15, y ≥ 0, x ≥ 0
(i) The line l1 : 3x + 2y = 150 passes through the points (50, 0) and (0, 75).
AB represents the line. Consider the inequality 3x + 2y ≤ 150.
Putting x = 0, y = 0 in 3x + 2y ≤ 150
⇒ 0 ≤ 150 which is true, shows that origin lies in this region.

The region lying below the line AB and the points lying on AB represents the inequality 3x + 2y ≤ 150.
(ii) The line l2 : x + 4y = 80 passes through the points (80, 0), (0, 20). This is represented by CD.
Consider the inequality x + 4y ≤ 80 putting
x = 0, y = 0, we get 0 ≤ 80, which is true.
⇒ Region lying below the line CD and the points on the line CD represents the inequality x + 4y ≤ 80
(iii) x ≤ 15 is the region lying on the left to
l3 : x = 15 represented by EF and the points lying on EF.
(iv) x ≥ 0 is the region lying on the right side of Y-axis and all the points on Y-axis.
(v) y ≥ 0 is the region lying above the X-axis and all the points on X-axis.
Thus, the shaded region in the figure is the solution of the given inequalities.