Math · Optimization

Simplex Method Calculator

Maximize a linear objective under ≤ constraints with two decision variables. Watch every pivot of the simplex tableau until the optimum.

c₁ (coefficient of x₁)

c₂ (coefficient of x₂)

Constraints (rows)

Constraints (each: a₁x₁ + a₂x₂ ≤ b)

Optimal value Z

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Standard form: maximize c₁x₁ + c₂x₂ subject to A x ≤ b, x ≥ 0.
Pivot rule: entering variable = most negative value in the Z-row; leaving variable = minimum ratio b/a for a > 0. Repeat until no negative entries remain in the Z-row.

Full tableaus

Every iteration shown with pivot highlighted in pink.

Basic variables

Optimal solution read directly from the final tableau.

Up to 4 constraints

Two decision variables, two to four constraints.

Step-by-step

Entering and leaving variables explained per pivot.

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