A gentleman farmer maniacally works on academic projects to raise funds for his true passion,farming.He has identified seven tasks and developed three time estimates (all in days)of the next big project on the farm,replacing the fence at the comedy pasture.Tasks,precedence requirements,and time estimates are shown in the table.What is the expected completion time of the project? $$\begin{array} { | l | l | l | l | l | }
\hline \text { Activity } & \begin{array} { l }
\text { Optimistic }
\end{array} & \begin{array} { l }
\text { Most Likely }
\end{array} & \begin{array} { l }
\text { Pessimistic }
\end{array} & \
\hline \text { time } & \text { time } & \text { time } & \text { Predecessor } \
\hline \text { Sorner Posts } & 4 & 5 & 6 & - \
\hline \text { Dig Holes } & 10 & 12 & 14 & \text { Corner Posts } \
\hline \text { Plant Posts } & 11 & 14 & 17 & \text { String Line } \
\hline \text { Weld Top Bar } & 8 & 11 & 14 & \text { String Line } \
\hline & & & & \text { Dig Holes, Plant } \
\hline \text { Paint } & 9 & 11 & 13 & \text { Posts } \
\hline \text { Tack Wire } & 9 & 12 & 16 & \text { Weld Top Bar } \
\hline
\end{array}$$
A) 32 days
B) 33 days
C) 34 days
D) 35 days

Question

A gentleman farmer maniacally works on academic projects to raise funds for his true passion,farming.He has identified seven tasks and developed three time estimates (all in days)of the next big project on the farm,replacing the fence at the comedy pasture.Tasks,precedence requirements,and time estimates are shown in the table.What is the expected completion time of the project? $$\begin{array} { | l | l | l | l | l | } 
\hline \text { Activity } & \begin{array} { l } 
\text { Optimistic }
\end{array} & \begin{array} { l } 
\text { Most Likely }
\end{array} & \begin{array} { l } 
\text { Pessimistic }
\end{array} & \
\hline \text { time } & \text { time } & \text { time } & \text { Predecessor } \
\hline \text { Sorner Posts } & 4 & 5 & 6 & - \
\hline \text { Dig Holes } & 10 & 12 & 14 & \text { Corner Posts } \
\hline \text { Plant Posts } & 11 & 14 & 17 & \text { String Line } \
\hline \text { Weld Top Bar } & 8 & 11 & 14 & \text { String Line } \
\hline & & & & \text { Dig Holes, Plant } \
\hline \text { Paint } & 9 & 11 & 13 & \text { Posts } \
\hline \text { Tack Wire } & 9 & 12 & 16 & \text { Weld Top Bar } \
\hline
\end{array}$$
A) 32 days
B) 33 days
C) 34 days
D) 35 days

Quizplus · Accepted Answer

To find the expected completion time for the project, we need to use the critical path method. 
First, we need to find the earliest start and finish times for each task. 
Starting with the first task, Sorner Posts, its earliest start time is 0 (since it has no predecessors) and its earliest finish time is 6 (using the most pessimistic estimate). 
Next, we do the same for each task, taking into account its predecessors and using the most pessimistic time estimate:

Dig Holes: earliest start time = 6, earliest finish time = 20 
Plant Posts: earliest start time = 17, earliest finish time = 34 
Weld Top Bar: earliest start time = 14, earliest finish time = 28 
Paint: earliest start time = 34, earliest finish time = 47 
Tack Wire: earliest start time = 28, earliest finish time = 44

The critical path is the longest path from the first task to the last task, which in this case is Sorner Posts -> Dig Holes -> Plant Posts -> Paint -> Tack Wire, with a duration of 44 days. Therefore, the expected completion time of the project is 33 days (the duration of the critical path's tasks added together). So, the best choice is B.

A Gentleman Farmer Maniacally Works on Academic Projects to Raise