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? $$\begin{array} { | l | l | l | l | }
\hline \text { Activity } & \text { Activity time } & \text { Workers Needed } & \text { Predecessor } \
\hline \text { A } & 10 & 1 & \
\hline \mathrm { B } & 4 & 2 & \
\hline \mathrm { C } & 7 & 3 & \mathrm {~A} \
\hline \mathrm { D } & 4 & 1 & \mathrm {~A} \
\hline \mathrm { E } & 8 & 2 & \mathrm {~B} \
\hline \mathrm { F } & 9 & 3 & \mathrm { C } , \mathrm { E } \
\hline \mathrm { G } & 13 & 1 & \mathrm { D } \
\hline \mathrm { H } & 14 & 2 & \mathrm { E } , \mathrm { G } \
\hline \mathrm { J } & 13 & 3 & \mathrm {~F} \
\hline \mathrm { K } & 10 & 1 & \mathrm { H } , \mathrm { J } \
\hline \mathrm { L } & 5 & 2 & \mathrm {~K} \
\hline
\end{array}$$
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? $$\begin{array} { | l | l | l | l | } 
\hline \text { Activity } & \text { Activity time } & \text { Workers Needed } & \text { Predecessor } \
\hline \text { A } & 10 & 1 & \
\hline \mathrm { B } & 4 & 2 & \
\hline \mathrm { C } & 7 & 3 & \mathrm {~A} \
\hline \mathrm { D } & 4 & 1 & \mathrm {~A} \
\hline \mathrm { E } & 8 & 2 & \mathrm {~B} \
\hline \mathrm { F } & 9 & 3 & \mathrm { C } , \mathrm { E } \
\hline \mathrm { G } & 13 & 1 & \mathrm { D } \
\hline \mathrm { H } & 14 & 2 & \mathrm { E } , \mathrm { G } \
\hline \mathrm { J } & 13 & 3 & \mathrm {~F} \
\hline \mathrm { K } & 10 & 1 & \mathrm { H } , \mathrm { J } \
\hline \mathrm { L } & 5 & 2 & \mathrm {~K} \
\hline
\end{array}$$
A) 54 days
B) 56 days
C) 58 days
D) 60 days

Quizplus · Accepted Answer

We can use the critical path method to find the fastest completion time. The critical path is the path through the network with the longest total duration, which determines the shortest time possible to complete the project.

- Activity A takes 10 days and has no predecessor.
- Activities B and D each require 1 worker and can be done simultaneously with A.
- Activity C requires 3 workers and can only start after A is completed, which takes 10 days.
- Activity E requires 2 workers and must wait until B is finished, which takes 4 days. It can be done simultaneously with F.
- Activity F requires 3 workers and can only begin once C and E are completed, which takes a total of 17 days.
- Activity G requires 1 worker and must wait until D is finished, which takes 10 days.
- Activity H requires 2 workers and must wait until E and G are finished, which takes 14 days.
- Activity J requires 3 workers and can only begin once F is completed, which takes 26 days.
- Activity K requires 1 worker and can only begin once H and J are finished, which takes 44 days.
- Activity L requires 2 workers and can only begin once K is finished, which takes 54 days.

Therefore, the fastest the project can be completed is 56 days, by using the critical path of A-D-G-H-J-K-L.

A Project Consists of Eleven Activities (All Times Are Given