Simplex-dual-sensitivity

AIMopt

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About this app

Master linear programming with a solver built for real understanding, not just answers.

This app solves linear programs (LPs) using the Big-M method and the Two-Phase method side by side, showing every tableau iteration along the way instead of just a final result. Whether you're a student learning operations research, an engineer optimizing resource allocation, an instructor preparing course material, or reviewing for exams, you get the full working shown step by step, exactly the way a textbook would present it — but computed instantly and without arithmetic mistakes.

SIMPLEX SOLVING
- Big-M Method and Two-Phase Method — pick either one, or solve the same problem both ways and compare
- Minimize or maximize, with any number of variables and constraints
- Mixed constraint types (≤, ≥, =) allowed together in the same problem
- Variables can be restricted to ≥ 0 or left completely free (unrestricted in sign), handled correctly throughout solving, sensitivity analysis, and duality
- Every tableau iteration displayed in full, including the Big-M method's symbolic M terms — not collapsed into a single "optimal solution" screen
- Automatic detection of infeasible problems, unbounded solutions, and problems with multiple optimal solutions
- Switch between decimal and exact-fraction display at any time, even after solving, without recalculating

SENSITIVITY ANALYSIS
- Find out how far an objective coefficient can change before the optimal basis itself would change
- Find the allowable range for a constraint's right-hand side, together with its shadow price
- See the full worked calculation, not just the final range — ratio-test tables are shown so you can follow exactly how each bound was derived, step by step
- Instantly re-solve the problem with a new coefficient or right-hand-side value if it falls outside the allowable range, and see the new optimal solution right away

DUAL PROBLEM
- Automatic dual formulation, generated directly from your primal problem's coefficients, constraint types, and variable restrictions
- Solve the dual as its own independent linear program — before solving the primal, after it, or instead of it entirely
- Cross-check in both directions: view the primal solution recovered directly from a solved dual, and the dual values read from a solved primal
- Complementary slackness and strong duality are checked and displayed automatically, so you can verify your work at a glance
- Move freely between primal and dual at any point in your workflow, solving either one whenever you like, in any order

BUILT FOR LEARNING, NOT JUST ANSWERS
- Clean, focused interface centered on the full step-by-step tableau history for every problem you solve
- Your current problem is saved automatically, so you can close the app and pick up exactly where you left off
- No ads, no account required, no clutter — just the mathematics, laid out clearly

WHO IT'S FOR
Students working through operations research, management science, or industrial engineering coursework. Instructors preparing worked examples or checking answer keys. Engineers and analysts running quick feasibility or optimization checks. And anyone who wants to actually see how the simplex method, duality theory, and sensitivity analysis fit together — not just get a number at the end.

Every solve shows its work: the initial tableau, every pivot with the entering and leaving variables, the optimal tableau, and the full reasoning behind every sensitivity range and dual value. If you've ever wondered why a textbook's shadow price is what it is, or what an objective coefficient's allowable range actually represents in practice, this app walks you through the exact calculation instead of hiding it behind a single result.

Download it, enter your linear program, and see the full picture — from the first tableau to the last, with the dual problem and sensitivity analysis always one tap away.

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