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Posted: **Tue May 10, 2022 7:07 pm**

: 4 15 Points The Following Diagram Shows A Branch And Bound Tree Search For An Integer Programming Maximization Proble 1 (33.07 KiB) Viewed 23 times

: 4 15 Points The Following Diagram Shows A Branch And Bound Tree Search For An Integer Programming Maximization Proble 2 (9.51 KiB) Viewed 23 times

4. (15 points) The following diagram shows a branch-and-bound tree search for an integer programming maximization problem. Each node has a number in parenthesis representing the search order and a value Z indicating the optimal LP relaxation value in that node. Assume that only nodes 5 and 6 yield integer solutions (i.e., their optimal LP relaxation solution turned out to be an integer solution) (1). 2-64 (2), Z = 58 (3), Z- 61 (4), Z-58.5 (5), Z-55 (6), Z = 56 (7),Z = 57

(b) Now consider that we branch on node 2 and create two new nodes: 8 and 9. Node 9 is infeasible and node 8 has Z = 56.5. What can you say about the optimal solution of the problem? If you cannot conclude that the optimal solution has been found, which node should we explore next, why?