Suppose that there is a software project that has the following activities.

$\backslash$table$[[$No$,$Activity,Duration,Predecessors$],[1,$Gathering Data,$4,-],[2,$Interview,$2,1],[3,$Analyze Data,$3,2],[4,$Define User Requirements,$4,3],[5,$Define System Requirements,$5,3],[6,$Develop Use Case Model,$1,4,5],[7,$Develop Class Diagram,$2,6],[8,$Develop State Machine Diagram,$4,7],[9,$Develop Activity Diagram,$3,7],[10,$Develop Sequence Diagram,$1,7],[11,$Develop ERD,$2,7],[12,$Prepare Analyze Report,$2,8,9,10,11],[13,$Design Database,$3,12],[14,$Design Software Architecture,$5,13],[15,$Develop Software,$53,14],[16,$Testing Software,$7,15],[17,$Fix problem,$2,15],[18,$Prepare Report,,$16,17],[,,,]]$

a$.$ Draw a network diagram

b$.$ Calculate the total duration by using Earliest Start $/$ Finish.

c$.$ Find the starting date of the first activity using Latest Start $/$ Finish, if the total duration was $100$ days.

d$.$ Find the slack values of all activities.

e$.$ Find the critical path.