Linear Programming Solver (Simplex Method)
Overview
The Linear Programming Solver demonstrates the Simplex method for solving optimization problems with linear constraints. Define objective functions and constraints, then watch as the Simplex algorithm pivots through basic feasible solutions to find the optimal solution. Visualize the feasible region and see how corner points represent basic feasible solutions. Essential for understanding operations research, resource allocation, and optimization theory.
Tips
- Linear programs maximize or minimize a linear objective function subject to linear constraints
- The Simplex method walks along edges of the feasible region visiting vertices
- The optimal solution (if it exists) is always at a vertex of the feasible region
- Slack variables convert inequalities to equalities for the Simplex tableau
- Watch the pivot operations transform the tableau towards optimality
- Try problems with 2 variables to see the feasible region visualized as a polygon
- Unbounded problems have no maximum, infeasible problems have no solution
- Applications include production planning, transportation, diet problems, portfolio optimization