Chapter 6 The Revised Simplex Method. This method is a modified version of the Primal Simplex Method that we studied in Chapter 5.
As in the standard format, bi≥0 for all i.
S’ = TS
T = ??????
After any number of iterations of the simplex method, the columns of the coefficient matrix corresponding to the basic variables at that iteration, comprise the identity matrix.
Initially, the last m columns of the coefficient matrix comprise the identity matrix.
S’ = [I,D’]
S = [B,D]
where B is the matrix constructed from the columns of the initial matrix corresponding to the current basic variables.
S’ = [I,D’] = TS = [TB,TD]
I = TB
from which we conclude that
T = B-1
new column = B-1 initial column
new RHS = B-1 initial RHS
S’ = B-1S = B-1 [M,I] = [B-1M,B-1I] = [B-1M,B-1]