= 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 $b$, then
$$
\begin{pmatrix}x_1\\x_3\end{pmatrix}
=\begin{pmatrix}2&5\\1&3\end{pmatrix}^{-1}\begin{pmatrix}33\\b\end{pmatrix}
=\begin{pmatrix}99-5b\\2b-33\end{pmatrix}.
$$
The dual prices remain $(1,1)$, so optimality persists exactly while both <basic variables> are nonnegative:
$$
\boxed{\frac{33}{2}\le b\le\frac{99}{5}.}
$$
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.
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