Answer the following questions using the network diagram.

$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$Predecessor$]],$Activity time$],[$A$,$None,$5],[$B$,$None,$2],[$C$,$B$,7],[$D$,$A C$,2],[$E$,$B$,6],[$F$,$D$,6],[$G$,$E$,5]]$

a$.$ Calculate the Forward and Backward passes of each activity.

b$.$ Determine the Critical Path of the Project.

c$.$ Determine the Project Completion Time.

d$.$ Calculate the Slack value of each activity.

To solve this problem using the given network diagram, we need to perform the following steps:

a$.$ Calculate the Forward and Backward passes of each activity:

Forward Pass $($Early Start Time$)$:

A $=0$

B $=0$

$($B $+$ duration of B$)$

$($C $+$ duration of C$,$ or A $+$ durations of A and C$)$

E $=7($B $+$ duration of B$)$

F $=7($D $+$ duration of D$)$

G $=13($E $+$ duration of E$)$

Backward Pass $($Late Finish Time$)$:

G $=13($Project Completion Time$)$

E $=8($G $-$ duration of G$)$

F $=8($G $-$ duration of G$)$

$($F $-$ duration of F$)$

C $=4($D $-$ duration of D$)$

B $=4($E $-$ duration of E$,$ or C $-$ duration of C$)$

A $=0($B $-$ duration of B$,$ or C $-$ durations of B and C$)$

b$.$ Determine the Critical Path of the Project:

The Critical Path is the longest path through the network diagram, where the total duration is maximized. From the calculations above, the Critical Path is

$,$ with a total duration of

time units.

Explanation:

Calculate the Forward and Backward passes of each activity:

Forward Pass $($Early Start Time$)$:

A $=0$

B $=0$

Step $2$

c$.$ Determine the Project Completion Time:

The Project Completion Time is the Late Finish Time of the last activity in the Critical Path, which is $13$ time units for activity G$.$

d$.$ Calculate the Slack value of each activity:

Slack is the amount of time an activity can be delayed without affecting the Project Completion Time. It is calculated as the difference between the Late Finish Time and Early Start Time for each activity.

A: Late Finish Time $-$ Early Start Time

$($No slack$)$

B: Late Finish Time $-$ Early Start Time

C: Late Finish Time $-$ Early Start Time $=4-5=-1($No slack$)$

D: Late Finish Time $-$ Early Start Time $=6-5=1$

E: Late Finish Time $-$ Early Start Time $=8-7=1$

F: Late Finish Time $-$ Early Start Time $=8-7=1$

G: Late Finish Time $-$ Early Start Time $=13-13=0($No slack$)$

The activities on the Critical Path $($A$,$ C$,$ E$,$ and G$)$ have no slack, while the other activities $($B$,$ D$,$ and F$)$ have some slack time

draw this