The Feasible Region is the set of all points satisfying all constraints of an optimization problem. For linear programs, it forms a convex polyhedron (potentially unbounded or empty). Properties: (1) convex for LP and convex programs; (2) optimal solutions occur at extreme points (vertices) for LP; (3) empty set indicates infeasibility; (4) unbounded region with objective improving indefinitely indicates unbounded problem. Understanding feasible region geometry aids solution interpretation and algorithm design. In integer programming, the feasible region consists of discrete points, typically a very small subset of LP relaxation vertices. Visualization of feasible regions (for 2-3 variables) provides intuition about problem structure and solution behavior.