Consider the problem: min: x + x 2x 4x2 3 subject to the three inequality constraints: X1 + X2 0, x1 + x2 0, and x + x 2. At the point (x, x) = (1, 1), the optimal dual solution: A = 1, A = 0, X3 = 3/2 - A = 1, A = 1/2, A3 = 1/2 -1, A = 0, A3 = 1/2 X A = 0, A = 0, X3 = 1 A = 0, A = 0, X3 = 0 A = 0, A -1, X3 = 1/2 They do not exist at this point.