Minimize Z = .4x1 + .5x2 --> Maximize -Z = -0.4x1 - 0.5x2

Solve using tabular form of simplex method in Excel.

Minimize Z= 0.4x1 + 0.5x2 subject to 0.3x1 + 0.1x2 + x3 = 2.7 0.5x1 + 0.5x2 + 14 = 6 0.6x1 + 0.4x2 -X +X6 = 6 and xi 0, X220, x3 0, X420, x 20, o > 0. As usual, introducing artificial variables enlarges the feasible region. Compare below the original constraints for the real problem with the corresponding constraints on (x1, x2) for the artificial problem. Constraints on (x1, x2) Constraints on (x1, x2) for the Real Problem for the Artificial Problem 0.3x1 + 0.1x2 0 x 20, x2 > 0 Introducing the artificial variable #4 to play the role of a slack variable in the second constraint allows values of (x1, x2) below the 0.5x +0.5x2 = 6 line in Fig. 4.4. Introduc- ing xs and g into the third constraint of the real problem (and moving these variables to the right-hand side) yields the equation 0.6x1 + 0.4x2 = 6 + Xs - To x220