= Simplex tableau
{title2=$x_B+B^{-1}A_Nx_N=B^{-1}b$}
A simplex tableau records the canonical constraint equations for a <simplex basis> and the canonical objective equation. For maximization use $z+\sum_j\rho_jx_j=z_0$, so a negative nonbasic objective-row coefficient is an improving direction. Constraint rows have an identity matrix in the basic columns. A <simplex method> pivot divides the leaving row by the pivot coefficient and eliminates the entering column from the other rows, including the objective row. The <simplex ratio test> chooses the largest feasible step. When all basic values and all $\rho_j$ are nonnegative, the objective equation directly proves $z\leq z_0$ for every nonnegative feasible vector.
Back to article page
