OPERATIONS MANAGEMENT

(19) Question 6 Consider the following initial simplex tableau: 2 2 11 22 13 $1 S2 83 a1 12 rhs BV 0 1 1 1 1 0 0 0 0 8 S1 0 1 2 -1 0 -1 0 1 0 4 ai 0 1 1 1 0 0 -1 0 1 1 12 1 -2M +1 -3M + 2 -1 0 M M 0 0 -5M 2 where M is a parameter that represents a big number and 11, 12 and 13 are positive decision variables, $1, 82 and $3 are slack or surplus variables, aand an are artificial variables, z is an objective function that must be maximised. Continue with the simplex algorithm until the final simplex tableau is found and deduce the optimal solution. If the LP problem is infeasible or unbounded, give the reason for this. If the LP problem has multiple optimal solutions, deduce the general optimal solu- tion. Important note: At each simpler tableau, indicate the entering variable, the leaving variable and the pivot element clearly