The attached search tree $($SearchTree$\_$Complete$\_$HW$03$Question odf$)$ is provided for a $4-$job scheduling problem. It is the "search tree" referred to some of the following questions.

Each node in the search tree displays a number which is the node's lower bound value for partial solution nodes and objective function value for complete solution nodes.

Each line denotes a branch, or$,$ link between a parent and a child node. The number on each line is the job index assigned to that position of the solution. Branching fills positions from left to right. So$,$ to read a solution, we have to come down from the root to that solution and read all numbers on the lines along that path.

Just to verify we read questions correctly from the search tree, match the following solutions to their lower bound or objective function values.

$13$

$31$

$1234$

$-34$

A$.$ This node doesn't exist because the jobs are assigned to positions from left to right here

B$.33$

C$.51$

D$.41$

Implement the B&B algorithm on the given search tree. You should explore six partial solutions $($given below$)$ throughout the course of the algorithm. Sort them in the order you explore them.

$2$

$43$

$4---$

$42--$

$23-$