Revised Dual Simplex Method. The steps of the revised dual simplex method (using matrix manipulations) can be summarized as follows:

Step 0. Let B0 = I be the starting basis for which at least one of the elements of XB0 is negative (infeasible).

Step 1. Compute XB = B-1b, the current values of the basic variables. Select the leaving variable xr as the one having the most negative value. If all the elements of XB are nonnegative, stop; the current solution is feasible

(and optimal).

Step 2.

(a) Compute zj - cj = CBB-1pj - cj for all the nonbasic variables xj.

(b) For all the nonbasic variables xj, compute the constraint coefficients 1B-1pj2r associated with the row of the leaving variable xr.

(c) The entering variable is associated with u = min i

e `

zj - cj 1B-1pj2r

` , 1B-1pj2r 6 0 f If all 1B-1Pj2r Ú 0, no feasible solution exists.

Step 3. Obtain the new basis by interchanging the entering and leaving vectors (pj and pr).

Compute the new inverse and go to step 1.

Apply the method to the following problem:

Minimize z = 3x1 + 2x2 subject to 3x1 + x2 Ú 3 4x1 + 3x2 Ú 6 x1 + 2x2 … 3 x1, x2 Ú 0