Bounded Two-variable Linear Program Workbench

How to use Bounded Two-variable Linear Program Workbench

Exact rational half-plane clipping intersects the entered finite box with every inequality or equality. A linear objective reaches an optimum at a remaining vertex; all tied optimal vertices are retained. Empty, point and line feasible sets are handled explicitly.

1. Enter constraint json (a, b, sense, limit), minimum x, maximum x, minimum y, maximum y, objective x coefficient, objective y coefficient.
2. Choose the stated convention and check the units and supported model.
3. Calculate, inspect the result, then copy or download it.

Good to know

• Exact-grid inputs are plain decimals with at most six places and magnitude≤1e9. Raw JSON number spelling is checked before conversion; decimal strings can preserve exact grid values. Exact rational intermediates are bounded to 8192 bits. At most 20 linear constraints. The finite x/y box is part of the model and must have positive width/height. No arbitrary expression parser, unbounded-region solver, integer programming or unique-solution claim. Constant constraints can retain or remove the whole region.
• Local calculation only; no input persistence or external lookup. Text/JSON is limited to 30000 characters and output to 1000000 characters. Numeric model inputs and precision/work limits are stated on this page. Approximate JSON numbers retain full stored values; exact arithmetic outputs retain decimal or fraction strings. Unsupported states fail explicitly.