When the Range Breaks - Sensitivity and Shadow Prices

Shadow prices are not extrapolation rules. This lesson pushes the RHS beyond the allowable range, shows the old basis becoming infeasible, and recomputes the LP.

highlighted = computed this step

Too far

Increase the first RHS by 5. Motivation: this deliberately moves past the allowable range endpoint.

\Delta b_1=5

Old basis candidate

The old basis candidate is (14/3, -1/3). Why: its negative coordinate violates the nonnegative bound, so the old certificate cannot be reused.

\text{old basis candidate is infeasible}

Recomputed optimum

The stale prediction is 13/3, but the recomputed optimum is (4, 0) with value 4. Interpretation: outside the range, recompute beats extrapolation.

z_{\text{new}}=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{range failure forces a new certificate}