The New Certificate - Sensitivity and Shadow Prices

After the active set changes, the certificate must change too. This lesson reads the new primal point and the new dual prices from the recomputed LP.

highlighted = computed this step

New primal

The recomputed primal point is (4, 0) with value 4. Motivation: once a bound is active, the active set has changed.

z_P=4

New dual

The recomputed dual prices are (0, 1). Why: the first old shadow price has dropped away and the second price carries the certificate.

y_{\text{new}}=0,1

Equality

The dual value is 4, matching the primal value. Interpretation: the new certificate replaces the old local rate.

z_P=z_D=4

Certificate note

RHS sensitivity is local: the shadow-price prediction is exact while the same basis remains primal feasible and dual feasible. Outside that range, the LP must be recomputed. Pixel positions are rounded for layout; every number shown is exact.

\text{the recomputed certificate is the proof}