General Linear Programming: Feasible Polygon and Optimal Solution

This example demonstrates how to find the optimal value of a linear objective function under a set of linear inequality constraints by working directly on the geometric feasible region (a polygon). It highlights that the optimum can be identified by checking candidate extreme points (typically the feasible vertices). The core mathematics includes general linear programming, linear inequalities, feasible region construction, objective-function maximization/minimization, and the vertex/extrama-based optimality idea. Construction details reflect the GeoGebra workflow: Sequence generates candidate data, RemoveUndefined and Unique clean and deduplicate intermediate results, Min/Max compute minimal and maximal objective values, Element extracts selected objects (such as vertices and matched values), and Segment builds boundary segments for the constraint lines. Frequency plus First/Last are used to organize candidates and retrieve meaningful endpoints, while Textfield places input parameters and computed outcomes onto the diagram. Key objects—regiones (feasible region), cortes (cuts/boundary segments), verticesregion (feasible vertices), posiblesextremos (possible extrema), valores, maximo, and minimo—connect the computation to visible geometry and labeled results. Suitable for advanced secondary school, introductory university optimization/operations research, and math modeling lessons focused on geometric intuition for LP/linear optimization.