 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

The unchanged reduced costs remain optimal for a maximization problem. The new basic solution is feasible exactly when $2-\alpha\geq0$ and $14+2\alpha\geq0$. Therefore
$$
\boxed{-7\leq\alpha\leq2.}
$$
The endpoints are included: one basic variable then vanishes, but feasibility and the reduced-cost certificate remain valid.

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