optional · interactive figures

Explore: the simplex method

The simplex method replayed pivot by pivot from the reference solution: tableau and path side by side, on four instances.

optional: nothing in the lab depends on itback to the slides

02 · explore

Simplex, one pivot at a time

Try: step with the button or the arrow keys (click the figure first); switch runs in the menu. Static versions: the walk, degeneracy, Klee–Minty.

What it shows. The reference solution's own pivots, replayed: the tableau with its entering column, ratio test and boxed pivot, beside the walk on the feasible region. The runs are recorded by slides/viz/traces/u02.py, which calls unit 02's reference initial_tableau, entering, leaving and pivot in exact fractions; uv run co viz 02 rebuilds them.

Unit 01's polygon, max 2x + y: the two pivots of "A walk on the example polygon".
max x + 3y: $y$ has the larger coefficient, and one pivot reaches $(0, 4)$.
Plus constraint 5, 3x − y ≤ 6, Bland's rule: the last pivot's ratio test ties between $s_1$ and $s_5$, so a zero-valued slack stays basic.
Klee–Minty, n = 2: all four corners, with the $y$-axis squeezed 20-fold to fit (its labels show true values).