$($b$)$A project manager discovers that his team has neglected to complete the network diagram for the project. The network shown in Figure Q$5.$ However, the project manager has some information available, specifically that each activity, labe has a different duration between one and seven weeks. Also, the slack time for each of the activities is known in Table

Table Q$5$

Duration $($we

Slack time wt

Figure Q$5$

Clues

There exists only one critical path, and it is the largest possible number given the possible durations shown.

Activity E has the smallest amount of slack that is greater than zero.

The early finish $($EF$)$ time for activity A is four weeks, and this does not equal the latest finish $($LF$)$ time. $($Note: The negative slack in the network.$)$

The slack in activity C is eight weeks.

The duration of activity F is greater than the duration of activity C by at least two weeks

Using the clues provided below,

i$.$ Determine the duration of each activity

$[5]$

ii$.$ Calculate the early start, early finish, latest start, and latest finish times for each activity.

$[10]$