You are the project manager for a new project which your company has won the bid. You have figured out the following dependencies:

Activity A can start immediately and similar same size activities to this one has occurred many times in the previous projects by $3$ weeks. Activity B can start after activity A is completed. This activity has many uncertainties, therefore by taking beta distribution, team member provided you with range of estimates $4,2,3$ weeks. Activity C can start after activity A is completed. This activity is considered the risky activity, thus by taking triangular distribution, you were provided by team member the following range of estimates $7,5,6$ weeks. Activity D can start after activity B is completed. This activity has $4$ units need to be completed in total, and historically each unit has been taken $2$ weeks of duration. Activity E is a path convergence by having predecessor activates D and C with FS relationship. This activity takes $4$ weeks.

YOUR WORK

$1.$ What is the duration of the Critical Path?

$2.$ What is the float of activity C$?$

$3.$ What is the f$1$oat of activity B$?$

$4.$ The resource working on activity C is replaced with another resource who is less experienced. The activity will now take $10$ weeks. How will this affect the project?

$5.$ After some arguing between stakeholders, a new activity F is added to the project. It will take $11$ weeks to complete and must be completed before activity E and after activity C$.$ Management is concerned that adding this activity will add $11$ weeks to the project. Another stakeholder argues the time will be less than $11$ weeks. Who is correct? Use the original information $($without the change to activity C listed in the previous question$)$ to answer this question.

$6.$ Based on the information in question $5$ how much longer will the project take?