$[10$ marks$]$ A small software development company has proposed the schedule given below for a client project.

$[$Recall that we are using the activity$-$on$-$arc formalism. Use the information in the table to construct an activity$-$on$-$arc PERT network diagram before answering the questions below.$]$

a$)$ What is the smallest number of days in which the project can be completed? Which activities are critical to on$-$time completion?

b$)$ The company wants to use a $5-$person team on this project to keep costs down. Is it possible to complete the project in the minimum time using only a $5-$person team?

Please answer the question using the Activity On ARC PERT Network Diagram before answering the questions.