A project consists of eleven activities (all times are given in days)and has worker requirements as indicated in the table.Assume that all six workers employed by this organization are generalists and are able to work on any of the tasks.What is the fastest the project can be completed? $\begin{array}{|l|l|l|l|}
\hline \text { Activity } & \text { Activity time } & \text { Workers Needed } & \text { Predecessor } \
\hline \text { A } & 10 & 1 & \
\hline \text { B } & 4 & 2 & \
\hline \text { C } & 7 & 3 & \text { A } \
\hline \mathrm{D} & 4 & 1 & \text { A } \
\hline \text { E } & 8 & 2 & \mathrm{~B} \
\hline \text { F } & 9 & 3 & \text { C,E } \
\hline \text { G } & 13 & 1 & \mathrm{D} \
\hline \text { H } & 14 & 2 & \text { E, G } \
\hline \text { J } & 13 & 3 & \mathrm{~F} \
\hline \mathrm{K} & 10 & 1 & \mathrm{H}, \mathrm{J} \
\hline \mathrm{L} & 5 & 2 & \mathrm{~K} \
\hline
\end{array}$

A)54 days
B)56 days
C)58 days
D)60 days

Question

A project consists of eleven activities (all times are given in days)and has worker requirements as indicated in the table.Assume that all six workers employed by this organization are generalists and are able to work on any of the tasks.What is the fastest the project can be completed? $\begin{array}{|l|l|l|l|}
\hline \text { Activity } & \text { Activity time } & \text { Workers Needed } & \text { Predecessor } \
\hline \text { A } & 10 & 1 & \
\hline \text { B } & 4 & 2 & \
\hline \text { C } & 7 & 3 & \text { A } \
\hline \mathrm{D} & 4 & 1 & \text { A } \
\hline \text { E } & 8 & 2 & \mathrm{~B} \
\hline \text { F } & 9 & 3 & \text { C,E } \
\hline \text { G } & 13 & 1 & \mathrm{D} \
\hline \text { H } & 14 & 2 & \text { E, G } \
\hline \text { J } & 13 & 3 & \mathrm{~F} \
\hline \mathrm{K} & 10 & 1 & \mathrm{H}, \mathrm{J} \
\hline \mathrm{L} & 5 & 2 & \mathrm{~K} \
\hline
\end{array}$

A)54 days
B)56 days
C)58 days
D)60 days

Quizplus · Accepted Answer

To determine the fastest completion time, we need to identify the critical path, which is the longest path of sequential activities in the project. This will determine the minimum number of days required to complete the project.

Using forward pass and backward pass calculations, we can determine the earliest start and finish times, as well as the latest start and finish times for each activity. The slack time for each activity can also be calculated by subtracting the duration from the difference between the latest and earliest finish times.

The critical path will have zero slack time for all activities, meaning any delay in these tasks will result in a delay in the overall project completion time.

In this case, the critical path is A - C - F - I - J - K with a total duration of 56 days, which is the minimum number of days required to complete the project.

Therefore, the best choice is B) 56 days as it is the fastest completion time.

A Project Consists of Eleven Activities (All Times Are Given