Linear Programming Calculator
Define an objective function and linear constraints, choose maximize or minimize, then compute the optimal decision variable values automatically instantly.
When needed, Big-M penalties create a valid starting basis automatically.
Choose whether to maximize or minimize the objective value Z.
Use x1, x2, x3... (or x_1) with numeric coefficients; spaces optional.
Uncheck to allow negative values; each xᵢ is internally modeled as xᵢ⁺−xᵢ⁻.
Enter one per line or comma-separated. Use <=, >=, or =, with a numeric right-hand side.
Equation Preview
Enter Z and constraints to preview the optimization problem here.
Substituted formatting updates live as you type.
Helping Notes
Required fields mirror common simplex tools: optimization type, objective function, constraints, and nonnegativity toggle. Type variables as x1, x2, … with relations ≤, ≥, or =. :contentReference[oaicite:1]{index=1}
For ≥ or =, the method uses Big-M artificial variables internally to start the algorithm. Results show the optimum, variable values, and status.
Results
Optimal Value
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Objective value at the optimum (Z*).
Variable Values
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Values of x₁, x₂, … at optimum.
Status
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Feasible/Optimal, unbounded, or infeasible; plus binding constraints if applicable.
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