Complementary Slackness At optimality, if a variable in one problem is positive, then the corresponding constraint in the other problem (its dual) must be tight (binding or active), If a constraint in one problem is not tight (unbinding or inactive), then the corresponding variable in the other problem (its dual) must be zero. Problem 1. Write a dual problem of the following, and find optimal solutions to both problems. Minimize 2x + subject to x1 3x2 + x2 + 5x3 + 2x4 + 2x3 + + 3x5 +354 2x1 - 21. 2x2 121 3x3 + I31 + 25 3 25 Problem 2. Write a dual problem of the following primal problem, and find optimal solution to the dual problem given that the optimal solution to the primal problem is x* = (0, 10.4, 0, 0.4). Maximize 2x1 + 4x2 + 3x3 + - + 4x4 12 3x22x3 + 3x4 subject to 3x1 + x2 + 23 21 2x1 21, + x2 + 3x3 23: 121 - 2700 24 10 24 >