Interactive lab¶
Here you can get your hands on linear programming. Pick an app: it opens full page. Drag the points and move the sliders; the ▶ button next to a parameter makes it move by itself. The problems come from the catalogue, with the numbers as exact fractions.
Linear functions, polyhedra and linear programming problems¶
-
Level lines
Move the cost vector and watch how the level lines and the gradient of a linear function change.
-
Half-spaces and polyhedra
Move the constraints: the feasible region is the intersection of half-planes, and its vertices follow.
-
The graphical method
Slide the level line toward the gradient until the last point that still touches the feasible region.
-
The outcomes of an LP problem
Unique optimum, multiple optima, unbounded, infeasible: change the data and recognize each case.
The simplex algorithm¶
-
The simplex method step by step
Follow the simplex method from vertex to adjacent vertex, with the pivot choice at every step.
Duality and the dual simplex¶
-
Weak and strong duality
Move a feasible primal and a feasible dual solution and watch the two objective values approach each other.
Matrix methods, sensitivity and geometry¶
-
Sensitivity analysis
Vary a coefficient and see how far the optimal basis stays optimal, and when it changes.