Past exam of the probability, statistics and options I course of the University of Oxford / 2009 / T / 1 / b

The basis and reduced costs stay unchanged when only the right-hand side changes. Its new basic values areThus for small $|\alpha |$,

The unchanged reduced costs remain optimal for a maximization problem. The new basic solution is feasible exactly when $2-\alpha \ge 0$ and $14+2\alpha \ge 0$. ThereforeThe endpoints are included: one basic variable then vanishes, but feasibility and the reduced-cost certificate remain valid.