Feasible region

Definition

A feasible region is the set of all possible points that satisfy a system of inequalities. It is typically represented as a shaded area on a graph.

5 Must Know Facts For Your Next Test

1. The feasible region can be bounded or unbounded depending on the system of inequalities.
2. Every point within the feasible region satisfies all of the given inequalities.
3. The boundaries of the feasible region are determined by the equality forms of the inequalities.
4. If there are no points that satisfy all inequalities, then no feasible region exists, indicating an infeasible problem.
5. Vertices or corner points of the feasible region often hold significance in optimization problems.

Review Questions

• What defines the boundaries of a feasible region?
• How can you determine if a point lies within the feasible region?
• What does it mean if there is no feasible region for a given system of inequalities?

Related terms

System of Inequalities: A set of two or more inequalities with the same variables.

Boundary Line: A line that represents where an inequality becomes an equality in a graph.

Vertex (Vertices): \text{ A point where two or more boundary lines intersect.}