Please answer all the part

Consider the following linear programming problem: Maximize 2x1 + 3x2 + 5x3 subject to X1 + 2x2 X1 2x2 + 2x3 = 6 X2 + 3x3 5 8 X1) *3 2 0. a. Write the dual problem. b. Solve the foregoing problem by the simplex method. At each iteration, identify the dual variable values and show which dual constraints are violated. C. At each iteration, identify the dual basic and nonbasic variables, along with the corresponding 3 x 3 dual basis. d. Show that at each iteration of the simplex method, the dual objective is "worsened." e. Verify that at termination, feasible solutions of both problems are at hand, having equal objective values and with complementary slackness holding