a) Use the simplex method to show that it has no feasible solution.
Maximize z = 4x1 + 5x2 + 3x3
Subject to:
x1 + x2 + 2x3 ≥ 20
15x1 + 6x2 - 5x3 ≤ 50
x1 + 3x2 + 5x3 ≤ 30
x1, x2, x3 ≥ 0
b) Show that the following linear programming problem is temporarily degenerate.
Minimize z = 2x1 + 2x2
Subject to:
4x1 + 3x2 ≤ 12
4x1 + x2 ≤ 8
4x1 - x2 ≤ 8
x1, x2 ≥ 0