The following LP is solved (using the big M method) and the optimal tableau is given below. e1 and e2 are the excess variables for the first and second constraints, and a1,a2,a3 are the artificial variables of the first, second and third constraints, respectively. maxz=4x1+x2s.t.3x1+x262x1+x24x1+x2=3x1,x20 a. Write the standard form of above LP. b. Write the big-M artificial LP. c. Find the dual LP. In addition, find the dual of the standard form LP in Part (a). What do you notice? d. Find cB,B1,B and cBB1 without any calculations. e. Find the optimal solution of the dual LP in using each of the following three methods: i. Strong Duality Theorem ii. Complementary Slackness Theorem iii. Reading off from tableau