Shadow Prices

One More Unit

A shadow price is a local rate. This lesson increases one RHS by a small exact amount, recomputes the LP, and checks that the value change matches the certificate price.

highlighted = computed this step

RHS change

Increase the first RHS by 1. Motivation: a shadow price asks how the objective changes when one resource moves locally.

Δb1=1\Delta b_1=1
One RHS increaseThe same basis remains feasible after increasing the first RHS by one.RHS changerhs Arhs Bzbase448/3changed543

Price prediction

The shadow price is 1/3, so the predicted objective increase is 1/3. Why: the same basis keeps the same dual price.

Δz=1/3\Delta z=1/3
One RHS increaseThe same basis remains feasible after increasing the first RHS by one.RHS changerhs Arhs Bzbase448/3changed543

New optimum

The recomputed point is (2, 1) with value 3. Interpretation: inside the range, the local price prediction matches the exact recompute.

znew=3z_{\text{new}}=3
One RHS increaseThe same basis remains feasible after increasing the first RHS by one.RHS changerhs Arhs Bzbase448/3changed543

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.

local RHS change, same certificate basis\text{local RHS change, same certificate basis}
One RHS increaseThe same basis remains feasible after increasing the first RHS by one.RHS changerhs Arhs Bzbase448/3changed543