Linear Programming Practice: How Many Solutions?

This GeoGebra example demonstrates how a linear programming/linear optimization problem can have different numbers of solutions depending on the geometric relationship among linear constraints. It highlights the key ideas of feasibility, the feasible region formed by intersecting linear boundaries, and the existence/uniqueness of solutions for a system implied by constraints. Conceptually, learners connect algebraic conditions with geometric configurations: constraints may intersect in a single point, in multiple points, along a segment, or yield no feasible solution, which directly affects how many candidate/optimal solutions exist. In GeoGebra, the construction typically involves creating the linear constraint objects (lines or their half-plane boundaries), identifying intersection points (solution candidates), forming the feasible polygon/region from the constraints, and then relating the target/optimization condition to determine the number of solutions. The original prompt provides no specific command list, so the description focuses on the standard geometric objects and workflow used to visualize and classify solution counts. Suitable for high school through early undergraduate courses on linear functions, linear systems, and introductory optimization.