Demonstration page

The simplex method

How linear programming finds the optimal solution — in four steps.

Now imagine millions of dimensions

This 3D polytope is already impossible to solve by inspection. Real problems — like optimising a year of 5-minute dispatch intervals across solar, battery, and cable — have millions of variables. Each constraint is a hyperplane, the feasible region is a polytope in million-dimensional space, and simplex still walks vertex to vertex. The maths is identical.

3D feasible polytope

Same rules: constraints form the shape, objective picks the direction, optimum is at a vertex.

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