Find the linear inequalities for which the shaded region in the given figure is the solution set.

First consider the linear equation 3x + 2y = 48, Observe that the shaded region and the origin both are on the same side of the graph of the line and (0, 0) satisfy the constraint 3x + 2y ≤ 48.

Now, consider x + y = 20, observe that the shaded region and the origin both are on the same side of the graph of the line and (0, 0) satisfy the constraint x + y ≤ 20.

Also, shaded region is in the first quadrant i.e. x ≥ 0 and y ≥ 0,

Hence, the linear inequalities are

3x + 2y ≤ 48

x + y ≤ 20

x ≥ 0

y ≥ 0