pls refer to the picture

A priva/ linear programming problem is: Maximize Z(X1,X2,X3,*4) = 3.5x3 - 5x2 + 4.5x, + 5x, subject to 2x3 + 5x1 - 3x2 + 4x4 4x1 + 9x3 - 7x4 S 19 13 6x2 + 2 x1 - 5X3 4 8x2 - 2 x3 + 5x4 12 *1 2 0, x2 - unconstrained, X3 - unconstrained, x, $ 0 a) Formulate the associated dual problem. [2 marks] b) Explain the complementary slackness theorem. [1 mark] c) The optimal solution for the dual problem is found to be ()1, V2. Va. Ya, the tasty, ty) = (0, 0.6328, 0. 9843, -1.36328, 0, 0, 0, 16.2460) where ty, to, to, and t, are slack variables. Complete the table below for the primal problem. Also, use information obtained in part a) if necessary. Primal Dual Optimal value Number of variables Number of constraints Optimal solution (0.0156, 1.8593, 1.4375, 0) Slack Shadow price Reduced Cost [3 marks] d') The right-hand side value of the fourth constraint in the dual model formulated in part a) is changed from 5 to 10, and the problem is then resolved. Assume the allowable increase is infinity for the right-hand side value of the fourth constraint. Write the new value of the objective function. [1 mark]