$7\mathrm{.}4$ The table below lists the time estimates and immediate predecessor$($s$)$ for each activity in a product marketing project that is to be scheduled using CPM$.$ Similar projects for other products have been accomplished in the past, so the activity times are fairly certain.

$($a$)$ Draw the CPM network diagram for the project, labeling all activities and times.

$($b$)$ Perform a forward pass and backward pass through the network to determine the critical path, the expected duration of the project, and the slack time for each activity.

Activity

$\backslash$table$[[,1,2,3,4,5,6,7,8,9],[$Activity time $($days$),1,4,3,7,5,2,6,9,4],[$Immediate predecessor,$-,1,1,1,2,3,4,5,6,4,7,8]]$