Complementary Slackness In Linear Programming
An animation showing a two-variable linear program with its feasible region and objective line sweeping toward the optimum. It highlights which constraints are binding at the optimal vertex, shows slack shrinking to zero on those constraints, and introduces the matching dual variables to illustrate the complementary slackness condition. Useful for students in optimization or operations research courses connecting primal geometry to dual variable interpretation.
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The prompt that made it
Explain complementary slackness visually using a two-variable linear programming problem. Show the feasible region, move the objective function toward the optimum, identify binding constraints, show slack becoming zero, and then introduce the corresponding dual variables.
Make the next one in this series
- Show the dual problem's feasible region and objective alongside the primal for the same example
- Animate weak and strong duality bounds tightening as primal and dual objectives converge
- Illustrate sensitivity analysis by shifting a constraint and showing the optimal vertex shift
