### Network Analysis ExerciseThis exercise requires an examination of a network diagram composed of various nodes and paths. We'll address several questions to understand the network's configuration and workflow.**Questions:**a. **How many different paths are there through the network?** b. **What is the number of the last node in the network?** c. **What is the difference in hours taken for the two paths when they connect at node 10?** d. **What is the difference in hours taken for the two paths when they connect at node 12?** e. **What is the expected duration of the entire project?** f. **What is the critical path?** Separate each node with a dash (–). g. **Which is the longest path?** Separate each node with a dash (–). ---### Diagram DescriptionThe provided network diagram consists of a series of nodes connected by paths with associated time values. These nodes range numerically, starting from node 1 and ending at node 12. Each path connecting these nodes is marked with a number representing the time (in hours) required to traverse the path.- **Node 1 connects to Node 2** with a path labeled 4 hours.- **Node 1 connects to Node 5** with a path labeled 10 hours.- **Node 2 connects to Node 4** with a path labeled 9 hours.- **Node 2 connects to Node 5** with a path labeled 8 hours.- **Node 4 connects to Node 7** with a path labeled 5 hours.- **Node 5 connects to Node 8** with a path labeled 7 hours.- **Node 6 connects to Node 9** with a path labeled 4 hours.- **Node 7 connects to Node 10** with a path labeled 2 hours.- **Node 8 connects to Node 10** with a path labeled 2 hours.- **Node 9 connects to Node 11** with a path labeled 6 hours.- **Node 9 connects to Node 12** with a path labeled 5 hours.- **Node 10 connects to Node 12** with a path labeled 3 hours.- **Node 11 connects to Node 12** with a path labeled 6 hours.This setup allows identification of paths, critical paths, and other network-specific queries relevant

NOTE: We are allowed to do the first three sub-parts only.

Answered: a. How many different paths are there…

Practical Management Science

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a. How many different paths are there through the network? b. What is the number of the last node in the network? c. What is the difference in hours taken for the two paths when they connect at node 10.