The simplex method reaches the flagship optimum by a short sequence of exact pivots. This lesson shows every tableau in that path and then repeats the process on the asymmetric example. The payoff is continuity: simplex lands on the same rational vertices the geometry book found.
highlighted = computed this step
Flagship sequence
The flagship sequence reaches (4/3, 4/3) with z=8/3. Why: the second pivot lands on the same vertex found geometrically.
z=8/3
Second pivot
The second pivot has ratio 4/3 and makes y basic. Why: the ratio test again preserves feasibility while z improves.
second ratio 4/3
Asymmetric example
The asymmetric sequence reaches (6/5, 8/5) with z=22/5. Why: the pivot rules generalize without changing the exact arithmetic.
z=22/5
Diagram note
The tableau path and the geometric vertex agree because both are recomputing the same LP. Pixel positions are rounded for layout; every number shown is exact.