Problem 5. Consider the following the following problem. Maximizez=3x1x2+6x3subjectto5x1+x2+4x3422x1x2+2x318x1,x2,x30 (a) (5 pts) Write the dual problem. (b) (10pts) Solve the primal problem by the primal simplex algorithm. Identify both the optimal primal and optimal dual solutions from the final tableau. (c) (5 pts) At each iteration in part (b), identify the dual solution and indicate which dual constraints are violated. Also, at each iteration, identify the 22 primal basis matrix and the 33 dual basis matrix. (d) (5 pts) Write the complementary slackness conditions and verify that these conditions are satisfied by the optimal solutions found in part (b). (e) (10 pts) Solve the problem in Python using CVXPY. Identify the shadow prices. Identify the reduced costs for the original variables. Interpret the two shadow prices and the three reduced costs