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

Explanation

Consider the line x + y = 4 .
We observe that the shaded region and the origin lie on the opposite side of this line and (0, 0) satisfies `x+y le4`. Therefore, we must have `x+y ge 4` as the linear inequation corresponding to the line x+ y = 4.
Consider the line x+ y = 8, clearly the shaded region and origin lie on the same side of this linear inequation corresponding to the line x + y 8.
Consider the line x = 5. It is clear from the graph that the shaded region and origin are on the left of this line and (0, 0) satisfy the constraint ` x le 5`.
Hence, ` x le 5` is the linear inequation corresponding to x = 5.
Consider the line y = 5, clearly the shaded region and origin are on the same side (below) of the line and (0, 0) satisfy the constrain ` y le 5`.
Therefore, `y le 5` is an inequation corresponding to the line y = 5.
We also notice that the shaded region is above the X-axis and on the right of the Y-axis i.e., shaded region is in first quadrant. So, we must have ` x ge 0, y ge 0`.
Thus, the linear inequations comprising the given solution set are
` x+y ge 4, x+y le 8, x le5, y le5, xge 0 and ge 0`.