What describes the feasible region in linear programming?

The feasible region in linear programming represents the set of all possible solutions that satisfy the constraints of the problem. These constraints are often represented as inequalities that define boundaries in a graphical representation. The intersection of these boundaries creates a polygonal area, where every point within this region corresponds to a solution that meets all specified constraints.

This region is critical because it defines the limits within which the optimal solution can be found. At each vertex of the feasible region, you can calculate the objective function’s value to determine which point maximizes or minimizes the objective function, aligning with the goal of the linear programming problem.

Other options refer to concepts that do not accurately define the feasible region. The first option describes a scenario where no solutions satisfy the constraints, while the second option suggests looking outside the defined boundaries, which is irrelevant for finding feasible solutions. Lastly, the fourth option focuses solely on the objective function without considering how it relates to the feasible solutions set forth by the constraints. Thus, the choice that best captures the essence of the feasible region is indeed the set of possible solutions that satisfy constraints.