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Linear Programming Calculator

Enter a linear objective and up to eight constraints to solve a two-variable linear program with x and y nonnegative. The two-phase simplex method reports an optimum, infeasibility or unboundedness and shows each pivot.

Objective coefficients (x, y)

One per line: a,b <= rhs, a,b >= rhs or a,b = rhs

Uses at most eight constraints and coefficients/right-hand sides within ±1,000,000. Both decision variables have x ≥ 0 and y ≥ 0. Use a comma between x and y coefficients; enter one inequality or equality per line.

A two-phase primal simplex solver for two variables. Numerical tolerance is used for floating-point pivots; near-degenerate problems can be sensitive to rounding. Infeasible, unbounded and iteration-limit cases are reported instead of an invented optimum.

How does the two-variable simplex calculator work?

It converts constraints into a feasible tableau, uses a Phase I objective when needed, then applies primal simplex pivots to optimize the requested objective. Variables x and y are constrained to be nonnegative.

Frequently asked questions

How does the two-variable simplex calculator work?

It converts constraints into a feasible tableau, uses a Phase I objective when needed, then applies primal simplex pivots to optimize the requested objective. Variables x and y are constrained to be nonnegative.

Are my objective and constraints uploaded?

No. The solver runs in this browser. Your objective and constraints are not sent to a server or saved by this tool.

What format should I use for constraints?

Enter one row per line, such as 1,1 <= 5 or 2,1 >= 4. The first number multiplies x, the second multiplies y, and both variables must be nonnegative.

What do infeasible and unbounded mean?

Infeasible means no point satisfies every entered constraint. Unbounded means a feasible direction lets the requested objective keep improving without a finite optimum.

Does the result prove my real-world model is correct?

No. It solves only the equations you entered. Check units, assumptions and whether the constraints properly describe your decision.