## The Reduced Costs, Dual Activities, and Current Tableau

The evaluation of reduced costs and the dual activities
is independent of problem structure.
For a basic solution, let *B* be the matrix composed of the basic
columns of *A* and let *N* be the matrix
composed of the nonbasic columns of *A*.
The reduced cost associated with the *i* th
variable is
(*c*^{T} - *c*^{T}_{B} *B*^{-1} *A*)_{i}

and the dual activity of the *j* th row is
(*c*^{T}_{B} *B*^{-1})_{j}

The Current Tableau is a section displayed when you specify either the
TABLEAUPRINT
option in the PROC LP statement or you specify the
TABLEAU option in
the PRINT statement.
The output contains a row for each basic variable
and a column for each nonbasic variable. In addition, there is a row
for the reduced costs and a column for the product

*B*^{-1} *b*

This column is labeled INV(B)*R.
The body of the tableau contains the matrix
*B*^{-1} *N*

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.