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A project has 15 activities, \(A-O\), that need to be completed.
The directed network that represents this project is shown below.
The activities are not labelled.
The activity table that could represent this project is
\(\text{Using trial and error:}\)
\(\Rightarrow B\)
A particular building project has ten activities that must be completed.
These activities and their immediate predecessor(s) are shown in the table below.
\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Activity} \rule[-1ex]{0pt}{0pt} & \textbf{Immediate predecessor(s)} \\
\hline
A & - \\
\hline
B & - \\
\hline
C & A \\
\hline
D & A \\
\hline
E & B \\
\hline
F & D, E \\
\hline
G & C, F \\
\hline
H & F \\
\hline
I & D, E \\
\hline
J & H, I \\
\hline
\end{array}
A directed graph that could represent this project is
The Sunny Coast cricket clubroom is undergoing a major works project.
This project involves nine activities: `A` to `I`.
The table below shows the earliest start time (EST) and duration, in months, for each activity.
The immediate predecessor(s) is also shown.
The duration for activity `C` is missing.
The information in the table above can be used to complete a directed network.
This network will require a dummy activity.
| This dummy activity could be drawn as a directed edge from the end of activity |
|
to |
| the start of activity |
|
. |
What is the minimum time, in months, that the project can be completed in? (1 mark)
a. `B\ text{to the start of activity}\ C.`
b. `text{Sketch network diagram.}`
`text{Duration of Activity C = 2 months}`
c. `text{Critical path:}\ BCDGI`
`text{Activities with a float time are activities}`
`text{not on critical path.}`
`:. \ text{Four activities are:}\ \ A, E, F, H`
d. `text{Completion time of}\ BCDGI = 20\ text{months}`
`text{Reduce the completion of}\ B\ text{by 3 months to create}`
`text{a new minimum completion time of 17 months.}`
A project involves nine activities, `A` to `I`.
The immediate predecessor(s) of each activity is shown in the table below.
| Activity | Immediate predecessor(s) |
|
| `A` | `-` | |
| `B` | `A` | |
| `C` | `A` | |
| `D` | `B` | |
| `E` | `B, C` | |
| `F` | `D` | |
| `G` | `D` | |
| `H` | `E, F` | |
| `I` | `G, H` |
A directed network for this project will require a dummy activity.
The dummy activity will be drawn from the end of
`text(Sketch network diagram:)`
`text(The dummy activity needs to be drawn)`
`text(from the end of activity)\ B\ text(to the start)`
`text(of activity)\ E.`
`=> B`
A project requires nine activities (A–I) to be completed. The duration, in hours, and the immediate predecessor(s) of each activity are shown in the table below.
The minimum completion time for this project, in hours, is
`text(Sketch the network:)`
`text(Completion time of paths:)`♦ Mean mark 49%.
`ABEGI = 4 + 3 + 5 + 4 + 3 = 19\ text(hours)`
`ACFGI = 4 + 7 + 2 + 4 + 3 = 20\ text(hours)`
`ADHI = 4 + 2 + 5 + 3 = 14\ text(hours)`
`:.\ text{Minimum completion time (critical path) = 20 hours}`
`=> C`
For a particular project there are ten activities that must be completed.
These activities and their immediate predecessors are given in the following table.
A directed graph that could represent this project is
Andy, Brian and Caleb must complete three activities in total (K, L and M)
The table shows the person selected to complete each activity, the time it will take to complete the activity in minutes and the immediate predecessor for each activity.
All three activities must be completed in a total of 40 minutes.
The instant that Andy starts his activity, Caleb gets a telephone call.
The maximum time, in minutes, that Caleb can speak on the telephone before he must start his allocated activity is
A. 5
B. 13
C. 18
D. 24
E. 34
The five musicians are to record an album. This will involve nine activities.
The activities and their immediate predecessors are shown in the following table.
The duration of each activity is not yet known.
There is only one critical path for this project.
The following table gives the earliest start times (EST) and latest start times (LST) for three of the activities only. All times are in hours.
The minimum time required for this project to be completed is 19 hours.
The duration of activity `C` is 3 hours.
| a. | |
b. `text(Possible critical paths are,)`
`ADGI, BEGI\ text(or)\ CFHI`
`:.\ text(Non-critical activities)`
`= 9 – 4 = 5`
c. `text(Critical activities have zero slack time.)`
`:. A\ text(and)\ C\ text(are non-critical.)`
`:. B − E − G − I\ \ text(is the critical path.)`
| d. | `text(Duration of)\ \ I` | `= 19 – 12` |
| `= 7\ text(hours)` |
e. `text(Maximum time for)\ F\ text(and)\ H`
`=\ text(LST of)\ I – text(duration)\ C – text(slack time of)\ C`
`= 12 – 3 – 1`
`= 8\ text(hours)`
The table below shows, in minutes, the duration, the earliest starting time (EST) and the latest starting time (LST) of eight activities needed to complete a project.
Which one of the following directed graphs shows the sequence of these activities?
A project will be undertaken in the wildlife park. This project involves the 13 activities shown in the table below. The duration, in hours, and predecessor(s) of each activity are also included in the table.
Activity `G` is missing from the network diagram for this project, which is shown below.
| a. | |
| b. | `text(EST of)\ H` | `= 4 + 3` |
| `= 7\ text(hours)` |
c.i. `A − F − I − M`
| c.ii. |  |
`G\ text(precedes)\ I`
`:. text(LST of)\ G = 20 – 4 = 16\ text(hours)`
`:. text(LST of)\ D = 16 – 2 = 14\ text(hours)`
d. `text(The statement will only be true if the crashed activity)`
`text(is on the critical path)\ \ A − F − I − M.`
e. `A − F − I − M\ text(is 37 hours.)`
`text(If)\ F\ text(is crashed by 2 hours, the new)`
`text(new critical path is)`
`C − E − H − G − I − M\ text{(36 hours)}`
`:.\ text(Minimum completion time = 36 hours)`
In the final challenge, each of four teams has to complete a construction project that involves activities `A` to `I`.
Table 1 shows the earliest start time (EST), latest start time (LST) and duration, in minutes, for each activity.
The immediate predecessor is also shown. The earliest start time for activity `F` is missing.
A section of the Farnham showgrounds has flooded due to a broken water pipe. The public will be stopped from entering the flooded area until repairs are made and the area has been cleaned up.
The table below shows the nine activities that need to be completed in order to repair the water pipe. Also shown are some of the durations, Earliest Start Times (EST) and the immediate predecessors for the activities.
It is more complicated to replace the broken water pipe (Activity `E`) than expected. It will now take four hours to complete instead of two hours.
Turning on the water to the showgrounds (Activity `H`) will also take more time than originally expected. It will now take five hours to complete instead of one hour.