What defines the area that satisfies every constraint in a linear programming problem?

The correct answer is the feasible region, which is a key concept in linear programming. The feasible region is defined as the set of all possible points that satisfy every constraint in a given linear programming problem. This area is typically represented graphically as a polygon on a coordinate plane, where each vertex corresponds to a potential solution.

In linear programming, constraints are represented by linear inequalities, and the intersection of these inequalities forms the feasible region. Solutions outside this area fail to meet at least one of the constraints and are therefore not considered valid. The objective of linear programming is often to optimize a certain function (the objective function) while confined within this feasible region.

Other terms, such as production zone, objective region, and solution area, may appear relevant but do not accurately describe the concept of the set of permissible solutions defined by the constraints. The term "production zone" might imply a specific area related to outputs or production levels but does not encompass the full set of feasible solutions. The "objective region" isn't a standard term in formal linear programming terminology, as it may refer to the area where the objective function is optimized rather than the constraints themselves. Lastly, "solution area" could be misleading as it potentially suggests any area where solutions might exist rather than