= Linear programming sensitivity within a fixed optimal basis
{title2=$v(b+\epsilon)=y^T(b+\epsilon)$}
For a <linear program> with unchanged cost and constraint matrix, an optimal <simplex basis> remains optimal while its basic solution remains feasible. Its <reduced costs> and dual certificate do not change. The new basic variables are $A_B^{-1}(b+\epsilon)$, and the objective is the displayed affine function, with $y$ the basis's dual solution. This gives an exact piecewise-affine sensitivity region, determined by nonnegativity of the basic variables, rather than merely a formal first derivative.
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