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 late finish for the Plant Posts activity? $$\begin{array} { | l | l | l | l | l | }
\hline \text { Activity } & \begin{array} { l }
\text { Optimistic } \
\text { time }
\end{array} & \begin{array} { l }
\text { Most Likely } \
\text { time }
\end{array} & \begin{array} { l }
\text { Pessimistic } \
\text { time }
\end{array} & \text { Predecessor } \
\hline \text { Corner Posts } & 4 & 5 & 6 & - \
\hline \text { String Line } & 7 & 8 & 9 & - \
\hline \text { Dig Holes } & 10 & 12 & 14 & \text { Corner Posts } \
\hline \text { Plant Posts } & 11 & 14 & 17 & \text { String Line } \
\hline \text { Weld Top Bar } & 8 & 11 & 14 & \text { String Line } \
\hline \text { Paint } & 9 & & 11 & \begin{array} { l }
\text { Dig Holes, Plant } \
\text { Posts }
\end{array} \
\hline \text { Tack Wire } & 9 & 12 & 16 & \text { Weld Top Bar } \
\hline
\end{array}$$
A) 13.3 days
B) 8 days
C) 20.83 days
D) 22 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 late finish for the Plant Posts activity? $$\begin{array} { | l | l | l | l | l | } 
\hline \text { Activity } & \begin{array} { l } 
\text { Optimistic } \
\text { time }
\end{array} & \begin{array} { l } 
\text { Most Likely } \
\text { time }
\end{array} & \begin{array} { l } 
\text { Pessimistic } \
\text { time }
\end{array} & \text { Predecessor } \
\hline \text { Corner Posts } & 4 & 5 & 6 & - \
\hline \text { String Line } & 7 & 8 & 9 & - \
\hline \text { Dig Holes } & 10 & 12 & 14 & \text { Corner Posts } \
\hline \text { Plant Posts } & 11 & 14 & 17 & \text { String Line } \
\hline \text { Weld Top Bar } & 8 & 11 & 14 & \text { String Line } \
\hline \text { Paint } & 9 & & 11 & \begin{array} { l } 
\text { Dig Holes, Plant } \
\text { Posts }
\end{array} \
\hline \text { Tack Wire } & 9 & 12 & 16 & \text { Weld Top Bar } \
\hline
\end{array}$$
A) 13.3 days
B) 8 days
C) 20.83 days
D) 22 days

Quizplus · Accepted Answer

To find the late finish for Plant Posts, we need to use backward pass and find the latest time it can finish without delaying the project. We start with the last activity, which is Tack Wire and its late finish is its pessimistic time, which is 16. Then, we work backward to find the late finish for the activities that immediately precede it. The late finish for Paint is 16-9=7, for Weld Top Bar is 7-14=-7, for Plant Posts is max(7-11,7-14) = -4, since both predecessors have late finishes that are earlier than their optimistic times, we take the maximum. Thus, the late finish for Plant Posts is -4, which means this activity cannot finish before the project is delayed. However, we need to add the duration of this activity to its late finish to find the late start, which is -4+17=13. So, the correct answer is 22, which is the late finish of Dig Holes activity.

A Gentleman Farmer Maniacally Works on Academic Projects to Raise