Construct a network diagram for the project below, determine the float$/$lack for each activity, and then identify the critical path. How many days are needed to complete the project?

$\backslash$table$[[$Activity$,$Task time $($in days$),$Preceding activilies$],[$A$,2,$None$],[$B$,4,$A$],[$C$,5,$None$],[$D$,4,$A$],[$E$,5,$A$],[$F$,6,$C$],[$G$,4,$C$],[$H$,7,$D$],[$I$,2$ I,D$],[$J$,5,$B$.$E$.$T$.],[$K$,4,$E$.$T$.$I.$]]$