$3.$ Draw the node network, perform the CPM calculations, mark the critical path, and complete the table below with an imposed finish date of $35$ and then $40$ days. $(20$ points$)$

With an imposed finish date of $35$ days:

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

$\backslash$hline Activity & Duration & IPA & ES & EF & LS & LF & TF $\backslash \backslash$

$\backslash$hline A & $3$ & $-$ & & & & & $\backslash \backslash$

$\backslash$hline B & $5$ & $-$ & & & & & $\backslash \backslash$

$\backslash$hline C & $6$ & A & & & & & $\backslash \backslash$

$\backslash$hline D & $9$ & A$,$ B & & & & & $\backslash \backslash$

$\backslash$hline E & $4$ & A$,$ B & & & & & $\backslash \backslash$

$\backslash$hline F & $6$ & B & & & & & $\backslash \backslash$

$\backslash$hline G & $5$ & C$,$ D & & & & & $\backslash \backslash$

$\backslash$hline H & $12$ & D$,$ E & & & & & $\backslash \backslash$

$\backslash$hline I & $7$ & D$,$ E$,$ F & & & & & $\backslash \backslash$

$\backslash$hline J & $9$ & F & & & & & $\backslash \backslash$

$\backslash$hline K & $10$ & G$,$ H$,$ I & & & & & $\backslash \backslash$

$\backslash$hline L & $6$ & I, J & & & & & $\backslash \backslash$

$\backslash$hline M & $4$ & G$,$ I & & & & & $\backslash \backslash$

$\backslash$hline N & $2$ & K & & & & & $\backslash \backslash$

$\backslash$hline

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