$9\mathrm{.}17$ Consider the following project tasks and their identified best, likely, and worst$-$case estimates of task duration. Assume the organization you work for computes TE based on the standard beta distribution formula. Calculate the TE for each of the following tasks $($round to the nearest integer$)$:

$\backslash$table$[[$Activity$,$Best,Likely,Worst,TE$],[$A$,4,5,10,],[$B$,4,6,9,],[$C$,2,5,8,],[$D$,5,8,10,],[$E$,12,16,20,],[$F$,6,10,12,],[$G$,5,9,14,],[$H$,14,16,22,],[$I$,10,14,20,],[$J$,1,2,5,]]$

Using the Description and Predecessors information from problem $9\mathrm{.}15$ and the calculated TE as the duration in days, construct the network activity diagram based on the following

Conduct both a forward and backward pass using AON notation. What is the estimated total duration for the project?

Identify all paths through the network. Which is the critical path?

Which activities have slack time?

Identify all burst activities and merge activities.