Linear Programming Solver (2 variables)
Enter a linear objective z in x and y, choose maximise or minimise, and list the constraints (each row like x + 2y ≤ 14, separated by semicolons). The calculator finds every pairwise intersection of the boundary lines, keeps those that satisfy all constraints, evaluates z at each, and plots the feasible region with the optimum marked.
Worked examples
Frequently asked questions
Why does the optimum always sit at a corner?
The objective is linear, so it cannot have interior extrema. On a bounded polygonal region it must be optimised at one of the vertices — the fundamental theorem of linear programming.
What if the feasible region is empty?
The calculator reports that no vertex satisfies every constraint. Re-check that the constraints are consistent — they should describe a non-empty polygon.
What relations are supported?
≤, ≥ and = (or <=, >=, =). Strict inequalities are not used in LP because the optimum sits on the boundary anyway.