Another RHS and a Mixed Change - Sensitivity and Shadow Prices

Sensitivity is not limited to one row, but it is still local. This lesson checks the second RHS and one simultaneous change by exact recomputation.

highlighted = computed this step

Second range

The second RHS has the same allowable delta interval, from -2 through 4. Why: this symmetric LP has symmetric RHS sensitivity.

\Delta b_2\in[-2,4]

Second RHS change

Increasing the second RHS by one gives point (1, 2) and value 3. Motivation: either resource can be tested through the same exact recompute.

z_{\text{second}}=3

Mixed change

Increasing the first RHS and decreasing the second RHS gives point (7/3, 1/3) and value 8/3. Interpretation: opposite changes can cancel in objective value when the two prices match.

z_{\text{mixed}}=8/3

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{same basis, same shadow prices}