System of Inequalities: Feasible Region

System of inequalities: finding the feasible region

The feasible region is where all constraints are satisfied simultaneously — the intersection of all individual shaded regions.

Step-by-step

Step 1 — Graph each inequality on the same axes with proper shading.

Step 2 — The feasible region is where all shadings overlap.

Step 3 — Find corner points where boundary lines intersect — these are candidates for optimal solutions in linear programming.

Example: $y \leq x + 4$, $y \geq -x + 2$, $x \geq 0$

Each constraint eliminates part of the plane. The surviving region (where all three are satisfied) is a triangle with vertices at $(0, 2)$, $(0, 4)$, and $(1, 3)$.

Try it in the visualization

Three constraint lines are shown. The feasible region highlights where all constraints overlap. Corner points are marked — these are the potential optimal solutions. Corner points of the feasible region are where boundary lines meet — these are the candidates for optimal solutions in linear programming.