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For First Responders · Linear Programming

Linear Programming for a network flow

Built for first responders planning or training for real incidents. Run fast what-if scenarios for response planning and training — no software to install in the field. Simulate a network flow live below — adjust the inputs and watch it respond, right in your browser.

Linear ProgrammingLive

optimize over a feasible region

Controls

Presets

Objective coeff. c₁ (x)

Objective coeff. c₂ (y)

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

max 3 x + 2 y s.t. x + y \leq 10, 2 x + y \leq 16, x + 3 y \leq 18, x, y \geq 0 \Rightarrow 26.0

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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Frequently asked questions

Is this good for first responders?: Yes — this version of "Linear Programming for a network flow" is framed for first responders planning or training for real incidents. Run fast what-if scenarios for response planning and training — no software to install in the field.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.