Problem $1.(9$ marks$).$ At a local university, the Student Commission on Programming and Entertainment $($SCOPE$)$ is preparing to host its first rock concert of the school year. To successfully produce this rock concert, SCOPE has listed the requisite activities and related information in the following table $($duration estimates measured in days$).$

$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$Predecess$],[$or$($s$)]],$Optimistic,$\backslash$table$[[$Most$],[$probable$]],\backslash$table$[[$Pessimisti$],[$c$]]],[\backslash$table$[[$A: Negotiate contract with selected$],[$musicians$]],---,8,10,15],[$B: Reserve site,$---,7,8,9],[\backslash$table$[[$C: Manage travel logistics for music$],[$group$]],$A$,5,6,10],[$D: Screen & hire security personnel,B$,3,3,3],[$E: Arrange advertising & ticketing,B$,$C$,1,5,9],[$F: Hire parking staff,D$,4,7,10],[$G: Arrange concession sales,E$,3,8,10],[,,,,]]$

a$.(7$ marks$)$ Draw the project network, indicating the earliest start, earliest finish, latest start, and latest finish day of each activity.

b$.(2$ marks$)$ What is the expected duration and variance of the critical path?