Linear Programming: Visualizing Feasible Region and Optimal Solution

① This GeoGebra example dynamically demonstrates the feasible region (a planar area defined by linear inequality constraints) and the optimal solution of a linear programming problem. ② Core mathematical concepts include linear inequalities, feasible region, objective function, optimality, vertex method, and the fundamental theorem of linear programming. ③ Construction highlights: based on the summary, it uses the Point command to create key points, and involves objects such as pic1 (possibly a background image), a, A, B, C, b, f, where a and b likely represent constraint coefficients or boundary lines, f is the objective function line, and A, B, C are vertices of the feasible region; dragging sliders or points allows dynamic observation of how the optimal solution changes. ④ Suitable for high school or early college mathematics instruction, providing an intuitive geometric understanding of linear programming and serving as an introductory demonstration for optimization problems.