Linear Programming (Simplex)

Solve a linear program — maximize or minimize a linear objective subject to linear constraints — with the two-phase Simplex method. Supports ≤, ≥, and = constraints, non-negative variables, and reports optimal solutions plus unbounded and infeasible cases. Everything runs locally in your browser.

Objective

Goal

Coefficients space-separated, one per variable

Constraints (one per line)

Format: coeffs… op rhs — e.g. 1 1 <= 12, 2 1 >= 5, 1 1 = 4. Variables are implicitly ≥ 0.

Result

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Linear programming optimizes a linear objective z = c·x over a convex polytope defined by linear constraints. The two-phase Simplex method walks along the polytope's vertices: Phase 1 finds an initial feasible basis using artificial variables (and detects infeasibility if they can't be driven to zero); Phase 2 improves the objective until no edge increases it further (reporting unbounded if an improving ray exists). It uses Bland's rule to avoid cycling. The optimum of an LP (when finite) is always attained at a vertex — and if there are several, along an edge or face between them. Pairs with the Matrix Calculator and Linear System Solver. Everything runs locally — nothing leaves your browser.