Consider the following project.
$$\begin{array} { | c | c | c | }
\hline \text { Activity } & \begin{array} { c }
\text { Immediate } \
\text { Processor }
\end{array} & \begin{array} { c }
\text { Activity Time } \
\text { (days) }
\end{array} \
\hline \text { A } & - & 6 \
\hline \text { B } & - & 8 \
\hline \text { C } & \text { A, B } & 5 \
\hline \text { D } & \text { B } & 4 \
\hline \text { E } & \text { C } & 7 \
\hline \text { F } & \text { C, D } & 3 \
\hline \text { G } & \text { D } & 6 \
\hline \text { H } & \text { E, F, G } & 5 \
\hline
\end{array}$$
-Determine the slack for activity D.
A) 2 days
B) 4 days
C) 6 days
D) 5 days

Question

Consider the following project.
 $$\begin{array} { | c | c | c | } 
\hline \text { Activity } & \begin{array} { c } 
\text { Immediate } \
\text { Processor }
\end{array} & \begin{array} { c } 
\text { Activity Time } \
\text { (days) }
\end{array} \
\hline \text { A } & - & 6 \
\hline \text { B } & - & 8 \
\hline \text { C } & \text { A, B } & 5 \
\hline \text { D } & \text { B } & 4 \
\hline \text { E } & \text { C } & 7 \
\hline \text { F } & \text { C, D } & 3 \
\hline \text { G } & \text { D } & 6 \
\hline \text { H } & \text { E, F, G } & 5 \
\hline
\end{array}$$
-Determine the slack for activity D.
A) 2 days
B) 4 days
C) 6 days
D) 5 days

Quizplus · Accepted Answer

Slack time is the amount of time that a task in a project can be delayed without causing a delay to subsequent tasks or the project completion date. To calculate the slack for activity D, we first need to determine the earliest start time (EST) and latest start time (LST) for each activity.- Activity A and B can start at day 0 because they have no predecessors. So, A finishes at day 6, and B finishes at day 8.- Activity C depends on A and B, so it can start at the latest of A and B's finish times, which is day 8. It takes 5 days, finishing at day 13.- Activity D depends only on B, so it can start after B finishes at day 8. It takes 4 days, finishing at day 12.- Activity E depends on C, starting after C finishes at day 13, and takes 7 days, finishing at day 20.- Activity F depends on C and D, so it can start after the latest of C and D's finish times, which is day 13 (from C). It takes 3 days, finishing at day 16.- Activity G depends only on D, so it can start after D finishes at day 12, and takes 6 days, finishing at day 18.- Activity H depends on E, F, and G, so it can start after the latest of these activities finishes, which is day 20 (from E). It takes 5 days, finishing at day 25.The project finishes at day 25, which is the finish time of activity H.To find the slack for D:- The earliest D can finish is day 12 (as calculated).- The latest D can finish without delaying the project is determined by its latest dependent activity's start time. Activity G, which depends on D, can start as late as day 18 (since it finishes at day 18 in the earliest scenario and has no slack). Since G takes 6 days, it must start by day 18 at the latest to finish by its own latest finish time. Therefore, D must finish by day 12 to allow G to start on time. However, if we consider the path through F (D -> F -> H), since F can start at day 13 and finish by day 16, and H can start by day 20, D has until day 13 to finish to allow F to start on time. This gives D a slack of day 13 - day 12 = 1 day, not matching any of the provided options directly.Given the options and the typical method of calculating slack, there seems to be a misunderstanding in the explanation process regarding the calculation of slack for D, as it directly depends on the latest start time of its immediate successor and the network's overall finish time. However, based on the standard approach to calculating slack and the provided options, the correct calculation involves determining the difference between the earliest and latest start times for D, considering the critical path and dependencies. Without a detailed critical path analysis including all latest start and finish times, pinpointing the exact slack for D based on the provided options requires assumptions about the project's constraints and dependencies not fully detailed in the explanation.

Consider the Following Project -Determine the Slack for Activity D