Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / T / 2 / c / i / Solution

In the usual linear programming sensitivity within a fixed optimal basis, retain the optimal basis $\{x_1,x_3\}$ while allowing its values to adjust. If the second resource amount is $b$, thenThe dual prices remain $(1,1)$, so optimality persists exactly while both basic variables are nonnegative:The optimal profit on that range is $33+b$. At the endpoints the basis is degenerate but remains optimal. If the wording is instead read as requiring the exact numerical production vector $(9,0,3)$ to remain unchanged and optimal, only $b=18$ does so; the standard allowable range concerns the basis and its adjusted solution.