Consider the following set of constraints:
- 2X1 + 3X2 = 3 (1)
4X1 + 5X2 ≥ 10 (2)
X1 + 2X2 ≤ 5 (3)
6X1+7x2 ≤ 3 (4)
4X1 + 8X2 ≥ 5 (5)
X1, x2 ≥ 0
For each of the following problem, develop the Z - row after substituting out the artificial variables:
(a) Maximize z = 5x1 + 6X2 subject to (1), (3), and (4).
(b) Maximize z = 2X1 - 7x2 subject to (1),(2), (4), and (5).
(c) Minimize z = 3X1 + 6X2 subject to (3), (4), and (5).
(d) Minimize z = 4X1 + 6X2 subject to (1), (2), and (5).
(e) Minimize z = 3X1 + 2X2 subject to (1) and (5).