PPolySim OS

Linear Programming

The optimization engine behind supply chains and airline scheduling. Constraints carve out a region, and the best answer always hides at a corner.

Linear ProgrammingLive

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Linear programming maximizes a linear objective subject to linear constraints. The constraints carve out a convex feasible region (shaded), and the optimum always sits at a corner. Slide the objective coefficients and watch the optimal vertex jump between corners — the geometric idea behind the simplex algorithm that runs global logistics and finance.

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Data Inspector

Optimal x6.00
Optimal y4.00
Objective value26.00

Governing equation

Reading this result: Maximizing 3·x + 2·y lands the optimum at the corner (6.0, 4.0) worth 26.0 — a linear objective over a convex region always peaks at a vertex, so sliding c₁/c₂ just makes the solution hop between corners.

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How it works

Linear programming maximizes a linear objective subject to linear inequality constraints. Those constraints define a convex feasible region, and a fundamental theorem guarantees the optimum lies at one of its vertices. Sliding the objective coefficients moves the optimal corner — the geometric intuition behind the simplex method used across operations research.

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Frequently asked questions

Is this linear programming visualizer tool really free?
Yes. Linear Programming runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.