A network diagram is a schematic display of the logical relationships among project activities and their sequencing. Given the following information, create a network diagram for the project using the activity$-$on$-$arrow$/$arrow diagramming method.

Node $1$ bursts into Nodes $2,3$ and $4.$

Node $2$ leads to Node $5$; Node $5$ leads to Node $6$; Node $6$ leads to Node $8.$

Node $3$ bursts into Node $5$ and Node $6$

Node $2$ and Node $3$ merge to form Node $5.$

Node $4$ leads to Node $7,$ Node $7$ leads to Node $6.$

Nodes $5,6$ and $7$ merge to lead to Node $8.$

The duration between Node $1$ and Node $2$ is $1$ Day

The duration between Node $1$ and Node $3$ is $2$ Days

The duration between Node $1$ and Node $4$ is $3$ Days

The duration between Node $2$ and Node $5$ is $4$ Days

The duration between Node $3$ and Node $5$ is $5$ Days

The duration between Node $3$ and Node $6$ is $4$ Days

The duration between Node $5$ and Node $6$ is $6$ Days

The duration between Node $6$ and Node $8$ is $3$ Days

The duration between Node $4$ and Node $7$ is $6$ Days

The duration between Node $7$ and Node $6$ is $2$ Days

Node $1$ is the starting point and Node $8$ is the finish point.

$(10$ Marks$)$

Based on your answer in Question $3\mathrm{.}1,$ identify the critical path for the project. $(2$ Marks$)$