Consider the following problem.

Maximize Z
2x1  x2  3x3, subject to x1  x2  x3
3 x1  2x2  x3 1 x1  2x2  x3 2 and x1 0, x2 0, x3 0.

Suppose that the Big M method (see Sec. 4.6) is used to obtain the initial (artificial) BF solution. Let x4 be the artificial slack variable for the first constraint, x5 the surplus variable for the second constraint, x6 the artificial variable for the second constraint, and x7 the slack variable for the third constraint. The corresponding final set of equations yielding the optimal solution is

(0) Z  5x2  (M  2)x4  Mx6  x7
8,

(1) x1  x2  x

4  x7
1,

(2) 2x2  x3  x7
2,

(3) 3x2  x

4  x5  x

6
2.