= Simplex objective update for a priced slack variable
{title2=$z+\sum_j(\rho_j-p\mathbf1_{j=k})x_j=z_0$}
If a variable $x_k$ gains an objective coefficient $p$, the new objective is $z=z_{\rm old}+px_k$. Substitute this in the old canonical objective equation and eliminate any remaining basic-column coefficients using the constraint rows. If $x_k$ is nonbasic, this simply subtracts $p$ from its objective-row coefficient. When a <slack variable> is sold, rename the old slack as the sales quantity; its equation already gives the correct equality and no new slack is added. Reoptimization can then start directly from the altered <simplex tableau>.
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