You are given the activity information below and the activity$-$on$-$node precedence diagram for a project at your company. $16$ points $(-4/$error$)$

a$)$ Determine the critical path and its duration. What is your initial estimate for project completion time? Show your work on the next page.

b$)$ Fill in the table on the next page to determine the earliest start $($ES$)$ time, the earliest finish $($EF$)$ time, the latest start $($LS$)$ time, the latest finish $($LF$)$ time, and the Slack for each project activity. Slack $=$ LS $-$ ES or LF EF$.$

$\backslash$table$[[$Activity Immediate Predecessor$($s$)$ Time $($days$),,],[$A$,--,6],[$B$,--,9],[$C$,$A$,3],[$D$,$A$,$ B$,5],[$E$,$C$,$ D$,9],[$F$,$D$,8],[$G$,$E$,$ F$,7],[$H$,$F$,15]]$

Note: This precedence diagram is posted as a separate pdf also.

Problem $3$ continues on the next page.

a$)$ Fill in the table with each path and show your work by calculating the time for each path in the table to determine the critical $($longest$)$ path$($s$).$ Add$/$delete rows in the table as needed. You must indicate the critical path and the estimated project completion time below the table.

Path Time

Critical Path $=$

Estimated Project

Completion $=$

b$)$ Fill in the ES & EF times in the table below working from Start to Finish. Then, fill in the LS & LF times working backwards from Finish to Start. After determining the ES$,$ EF$,$ LS$,$ & LF times, calculate the Slack time for each activity using both Slack $=LS-ES$ and Slack $=LF-EF.$ Note: Both calculations must give you the same answers.

Activity ES EF LS LF Slack

A

B

C

D

E

F

G

H