(a) Use the KKT conditions to derive an optimal solution directly. (b) Now suppose that this problem is to be solved by the modified simplex method. Formulate the linear programming problem that is to be addressed explicitly, and then identify the additional complementarity constraint that is enforced automatically by the algorithm. (c) Without applying the modified simplex method, show that the solution derived in part (a) is indeed optimal (Z=0) for the equivalent problem formulated in part (b). I (d) Apply the modified simplex method to the problem as formulated in part (b). 1. Solve the problem using the instructions in 13.7-4 (b) and (d) only. Provide your LP formulation calculation/working steps and additional complementarity constraints on a Word file. 2. For (d), enter the LP formulation you obtained in (b) into the app on Math Auditor (see below) to use the simplex tableau to obtain an optimal solution. Copy the output table(s) and optimal solution into your Microsoft Word file