Generate the dual simplex iterations for the following problems (using TORA for convenience), and trace the path of the algorithm on the graphical solution space.

(a) Minimize z = 2x1 + 3x2 subject to 2x1 + 2x2 … 3 x1 + 2x2 Ú 1 x1, x2 Ú 0

(b) Minimize z = 5x1 + 6x2 subject to x1 + x2 Ú 20 4x1 + x2 Ú 40 x1, x2 Ú 0

(c) Minimize z = 4x1 + 2x2 subject to x1 + x2 = 10 3x1 - x2 Ú 20 x1, x2 Ú 0

(d) Minimize z = 2x1 + 3x2 subject to 2x1 + x2 Ú 30 x1 + x2 = 20 x1, x2 Ú 0