Find the linear inequations for which the shaded region in fig. 15.40 is the solution set.

Explanation

We have seen that the shaded region and origin are on the same side of the line 3x + 4y = 12.


For (0,0) we have 0 + 0 - 12 < 0. So the shaded region satisfies the inequality 3x + 4y ≤ ≤12.


We have seen that the shaded region and origin are on the same side of the line 4x + 3y =12 For (0,0) we have 0 + 0 -12 < 0.

So the shaded region satisfies the inequality 4x + 3y ≤ ≤12.

Also , the region lies in the first quadrant

Therefore x ≥ ≥ 0 and y ≥ ≥0

Thus the linear inequation comprising the given solution set are +4y ≤12, 4x + 3y ≤ 12, x ≥ 0, y ≥0