Given the table below, assuming that there are only $8$ resources available at any time:

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

$\backslash$hline Activity & $\backslash$begin$\{$tabular$\}\{$c$\}$

Duration $\backslash \backslash$

$($weeks$)$

$\backslash$end$\{$tabular$\}$ & Dependency & Resources $\backslash \backslash$

$\backslash$hline A & $12$ & & $4\backslash \backslash$

$\backslash$hline B & $7$ & & $2\backslash \backslash$

$\backslash$hline C & $4$ & & $3\backslash \backslash$

$\backslash$hline D & $7$ & A & $5\backslash \backslash$

$\backslash$hline E & $1$ & B & $3\backslash \backslash$

$\backslash$hline F & $3$ & B$,$C & $4\backslash \backslash$

$\backslash$hline G & $6$ & D$,$E & $4\backslash \backslash$

$\backslash$hline I & $2$ & D$,$E & $5\backslash \backslash$

$\backslash$hline J & $4$ & F & $3\backslash \backslash$

$\backslash$hline K & $6$ & G & $3\backslash \backslash$

$\backslash$hline

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

a$)$ Provide the full network diagram $(6$ marks$)$

b$)$ Provide the original Gantt chart with all resources $(6$ marks$)$

c$)$ Provide the detailed steps $($how and why$)$ for the updated the schedule based on resource constraints $(\backslash (121/3\backslash )$ marks$)$

d$)$ Provide the final Gantt chart $(6$ marks$)$

e$)$ What is the final project duration? $(3$ marks$)$