Please give detailed solutions step by step Thanks

[answerhappygod]

Please give detailed solutions
step by step
Thanks

Please Give Detailed Solutions Step By Step Thanks 1 (97.24 KiB) Viewed 36 times

Consider the integer optimisation problem X1 + x2 max 3-X2 58 16 subject to - X1 + 3x2 + 2x2 = 12 X1,x2 2 0 and integer The LP relaxation of the integer optimisation problem has been solved using the Simplex method and the optimal tableau is as follows in Table 3. Basis X1 X2 х3 X4 RHS 1 X2 18 0 8 و 1 0 1 2 6 X1 1 8 27 3 f 0 0 19 14 18 54 3 Table 3: Tableau for the LP relaxation of integer optimisation problem in Question 4. a) Generate a Gomory cut from the f row, add it to the optimal tableau and re-optimise using the dual simplex method. Choose the variables with the smallest possible index as entering and leaving variable. (40 marks) b) Is this the optimal solution of the integer programme? What does this mean? (10 marks) c) Instead of using Gomory cuts, consider solving the problem by Branch and Bound. State the branching variables and the branches to be added to the optimal solution of Table 3. (20 marks) d) Solve the LP of the left and the right branch either using (dual) simplex iterations or using an LP solver and thus find (bounds for the optimal solution of the IP. (30 marks)