1. The problem is to understand and describe the feasible region for a given system of inequalities or constraints in an optimization or linear programming problem. 2. The feasible region is the set of all points $(x, y)$ that satisfy all the inequalities simultaneously. 3. To find the feasible region, plot each inequality as an equation (boundary line) and determine which side of the line satisfies the inequality. 4. For example, given inequalities such as $x \geq 0$, $y \geq 0$, and $x + y \leq 5$, the feasible region is the intersection of all these half-planes. 5. Geometrically, this region represents all possible $(x,y)$ pairs that do not violate any constraints. 6. The feasible region is typically a convex polygon (or unbounded region) that can be shaded to represent all solutions to the system. 7. Identifying corner points (vertices) of the feasible region is important as optimum values of linear functions occur at these points. 8. Summary: The feasible region is the set of all points satisfying all constraints, found by graphing each inequality and taking their intersection.