What term describes the set of all possible solutions that meet the constraints in linear programming?

The term that describes the set of all possible solutions that meet the constraints in linear programming is known as the feasible region. In the context of linear programming, constraints are expressed as linear inequalities, and the feasible region is the graphical representation of these inequalities. It includes all the points (possible solutions) that satisfy all the constraints simultaneously.

The feasible region is crucial because it determines the limits within which the objective function can be optimized, whether that's to maximize or minimize a certain value. This region can be represented visually in multidimensional space, typically as a polygon in two dimensions or a polytope in higher dimensions. Solutions that lie within this region are valid, whereas solutions outside of it do not satisfy the given constraints.

In contrast, other terms such as decision boundary, optimization space, and solution set refer to different concepts in the realm of optimization and linear programming. The decision boundary, for instance, typically refers to the limits that separate different regions based on conditions or criteria rather than the feasible solutions themselves. The term optimization space is more general and does not specifically denote the set of feasible solutions. Similarly, the solution set might suggest general solutions but lacks the specific connotation of satisfying all constraints, which is pivotal in defining the feasible region.