The certificate is not special to the flagship LP. This lesson repeats the construction on the asymmetric example from the earlier books. The primal point, dual prices, and equality are all recomputed from the new coefficients.
highlighted = computed this step
Asymmetric primal
The asymmetric primal optimum is (6/5, 8/5) with z=22/5. Why: this is the same problem that geometry and simplex already solved.
zP=22/5
Asymmetric dual
The asymmetric dual optimum is (1/5, 3/5) with z=22/5. Why: the resource prices give an exact upper bound at the optimum.
zD=22/5
Second certificate
Both objectives equal 22/5. Why: the certificate works on a different LP without changing the exact arithmetic.
zP=zD=22/5
Diagram note
The asymmetric display is recomputed from build dual and strong duality, not copied from the flagship. Pixel positions are rounded for layout; every number shown is exact.