# Tableau

(pl. tableaux). A detached coefficient form   of a system of equations, which can change from $LaTeX: \textstyle x+Ay=b$ to $LaTeX: x'+A'y'=b'.$ The primes denote changes caused by multiplying the first equation system by the basis inverse (a sequence of pivots in the simplex method). Although the exact form varies (e.g., where to put $LaTeX: b$), the following is fairly standard:
 Nonbasic Variables Basic Variables Basic Level at lower bound at upper bound | superbasic name (or index) $LaTeX: x_B$ coefficients are negatives of the rates of substitution obj $LaTeX: -z$ reduced costs | Lagrange multiplier