Description: The feasible region is a fundamental concept in mathematical optimization, referring to the set of all possible solutions that satisfy the constraints imposed by a specific problem. In simpler terms, it is the area where all combinations of variables that meet the necessary conditions for a solution to be considered valid are found. This region can be graphically represented in a multidimensional space, where each dimension corresponds to a variable of the model. The main characteristics of the feasible region include its shape, which can be convex or non-convex, and its size, which can vary depending on the complexity of the problem and the constraints imposed. Identifying this region is crucial as it allows analysts and researchers to focus their efforts on finding optimal solutions within a defined framework, thus avoiding solutions that are not viable. Furthermore, the feasible region plays an important role in linear programming theory and other optimization methods, as the ultimate goal is to find the optimal point within this area that maximizes or minimizes an objective function. In summary, the feasible region is an essential component in the optimization process, providing a clear framework for the search for effective solutions.
