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
Solution space for Problem1, Set 4.4a


Subject to
2x1 + 2x2 ≤ 30
X1 + 2x2 ≥ 10
X1, x2 ≥ 0
(b) Minimize z = 5x1 + 6x2
Subject to
X1 + x2 ≥ 2
4x1 + x2 ≥ 4
X1, x2 ≥ 0
(c) Minimize z = 4x1 + 2x2
Subject to
X1 + x2 = 1
3x1 - x2 ≥ 0
(d) Minimize z = 2x1 + 3x2
Subject to
2x1 + x2 ≥ 3
X1 + x2 = 2
X1, x2 ≥ 0