A company must perform a maintenance project consisting of seven activities.The activities,their predecessors and their respective time estimates are presented below: $\begin{array}{|l|l|l|l|}
\hline & & \text { Immediate } & \
\hline \text { Activity } & \text { Designation } & \text { Predecessor } & \text { Time in Days } \
\hline \text { Break down both machines } & \text { A } & \text { None } & 3 \
\hline \text { Clean machine 1 } & \text { B } & \text { A } & 3 \
\hline \text { Clean machine 2 } & \text { C } & \text { A } & 3 \
\hline \text { Re-set machine 1 } & \text { D } & \text { B } & 4 \
\hline \text { Re-set machine 2 } & \text { E } & \text { C } & 2 \
\hline \text { Re-calibrate both machines } & \text { F } & \text { D and E } & 1 \
\hline \text { Final test } & \text { G } & \text { F } & 1 \
\hline
\end{array}$
Using the Single Time Estimate CPM procedure,which activities have slack in this project?
A)A,B,C
B)B,D
C)Only C
D)C,E
E)F,G

Question

Quizplus · Accepted Answer

To find out the slack of the activities, we need to first calculate the Earliest Start Time (EST) and the Latest Start Time (LST) for each activity using the Single Time Estimate CPM procedure.

$\begin{array}{|l|l|l|l|l|l|l|l|} \hline & & & & & & & \ [-2.5ex] & & & \text{EST} & \text{LST} & & & \ [0.5ex] \hline \text{Activity} & \text{Predecessor} & \text{Time} & \text{Optimistic} & \text{Pessimistic} & \text{Time Estimate} & \text{Slack} & \text{Critical Path} \ [0.5ex] \hline A & - & 3 & 3 & 3 & 3 & 0 & Yes \ \hline B & A & 3 & 6 & 6 & 6 & 3 & No \ \hline C & A & 3 & 6 & 6 & 6 & 3 & No\ \hline D & B & 4 & 9 & 9 & 9 & 3 & No \ \hline E & C & 2 & 8 & 8 & 8 & 6 & No \ \hline F & D,E & 1 & 18 & 14 & 15 & 6 & Yes \ \hline G & F & 1 & 19 & 15 & 16 & 0 & Yes \ \hline \end{array}$

The activities with slack are those where the LST is greater than the EST. From the table, we can see that the activities with slack are: B, D, and E. Therefore, the answer is D.

A Company Must Perform a Maintenance Project Consisting of Seven