4. 8 marks Solve the following LP problems using the simplex method. At each step please state the entering and leaving variables and the current basic feasible solution. Clearly state the optimal solution and the optimal value. To get credits for this problem, you should use Anstee's rule: . Choose the entering variable with the largest positive coefficient. . If there is a tie, then choose the one with the smaller subscript. . If there is a choice of leaving variable, then choose the one with the smallest subscript. For more discussion on Anstee's rule and related examples, see the self-study parts of the lecture notes of Lec9 for MWF class, Lec 6 for TuThu class. (a) 4 marks Maximise z = 2x1 + 3x2 + 3x3, subject to 3x1 60 +4x3 IA IA IA 10 2x1 -2102 +5x3 15 and $1, $2, 23 2 0. This problem requires 2 pivots. (b) 4 marks Maximise z = 3x1 + 2x2 + 4x3, subject to +2 +213 2x1 +313 -J OT IALAIA 2x1 +22 +313 and X1, 22, 23 2 0. This problem requires 3 pivots