Using the artificial constraint procedure introduced in Problem 3, solve the following problem by the dual simplex method. In each case, indicate whether the resulting solution is feasible, infeasible, or unbounded.
(a) Maximize z = 2x3
Subject to
- x1 + 2x2 - 2x3 ≥ 8
- x1 + x2 + x3 ≤ 4
2x1 - x2 + 4x3 ≤ 10
X1, x2, x3 ≥ 0
(b) Maximize z = x1 - 3x2
Subject to
X1 - x2 ≤ 2
X1 + x2 ≥ 3
2x1 - 2x2 ≥ 3
X1, x2 ≥ 0
(c) Minimize z = - x1 + x2
Subject to
X1 - 4x2 ≥ 5
X1 - 3x2 ≤ 1
2x1 - 5x2 ≥ 1
X1, x2 ≥ 0
(d) Maximize z = 2x3
Subject to
- x1 + 3x2 - 7x3 ≥ 5
- x1 + x2 - x3 ≤ 1
3x1 + x2 - 10x3 ≤ 8
X1, x2, x3 ≥ 0