$1.$ A project has been defined to contain the following list of activities along with their required times for completion.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Activity No$.$ & Activity & Time $($Weeks$)$ & Immediate Predecessors $\backslash \backslash$

$\backslash$hline $1$ & Collect requirements & $2$ & $-\backslash \backslash$

$\backslash$hline $2$ & Analyze processes & $3$ & $1\backslash \backslash$

$\backslash$hline $3$ & Analyze data & $3$ & $2\backslash \backslash$

$\backslash$hline $4$ & Design processes & $7$ & $2\backslash \backslash$

$\backslash$hline $5$ & Design data & $6$ & $2\backslash \backslash$

$\backslash$hline $6$ & Design screens & $1$ & $3,4\backslash \backslash$

$\backslash$hline $7$ & Design reports & $5$ & $4,5\backslash \backslash$

$\backslash$hline $8$ & Program & $4$ & $7,7\backslash \backslash$

$\backslash$hline $10$ & Test and document & $8$ & $8,9\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

a$.$ Draw a network diagram for the activities.

b$.$ Calculate the earliest expected completion time.

c$.$ Show the critical path.

d$.$ What would happen if activity $6$ were revised to take $6$ weeks instead of $1$ week?