(a) Shara was given a maximization LP to solve by using the simplex method. Her optimal tableau is shown below. Z X1 X2 Basic Row Variable No. Z X1 1 S2 2 X2 3 WNO OOON 0 1 0 0 Oolo Coefficient of Si S2 0 0 1 0 3 1 -3/2 0 S3 1 0 -1 1/2 Right Side 18 4 6 3 1 (i) (ii) (111) Write down Shara's optimal solution. [2] Shara's friend Xhara says that the LP has multiple optimal solutions. How does Xhara know this? [3] Khara, a friend of both Shara and Xhara, overhears the conversation and is interested in seeing another optimal solution. Use Shara's optimal tableau to produce another optimal solution for Khara. [5] Phara, a friend of Shara, Xhara and Khara, is curious about what the objective function for the LP could be. Determine the objective function for Phara. [5] (iv) (b) Consider the following problem. st Max z = -x1 + 2x2 + x3 3x2 + x3 = 120 X1 - X2 120 X2, X2, X3 > 0 Using the Big M method with M = 400, construct the complete initial simplex tableau for the simplex method and write down the initial basic feasible solution. Also identify the entering nonbasic variable and the leaving basic variable. [7]