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Networks, STD2 EQ-Bank 25

The construction of a new reptile exhibit is a project involving nine activities, \(A\) to \(I\). The network diagram below shows the activities and their completion times in weeks. Some values are missing.

The Gantt chart below has been created for this project.
  


  
  1. Using the Gantt chart, identify the critical path.   (1 mark)
  2. Use the Gantt chart to determine the missing values in the network diagram.   (2 marks)
  3. Activity \(E\) is delayed by 8 weeks. Using the Gantt chart, explain whether this will affect the minimum completion time of the project.   (2 marks)
Show Answers Only

a.    \(ACDFGI\)

b.    \(\text{B} = 5 \text{ weeks, H} = 7 \text{ weeks}\)

c.    \(\text{From the Gantt chart, activity E has a float of 6 weeks (see the dashed}\)

\(\text{extension from week 10 to 16).}\)

\(\text{The delay of 8 weeks exceeds the float of 6 weeks.}\)

\(\text{The project will be delayed by } 8-6 = 2 \text{ weeks.}\)

\(\text{New minimum completion time} = 25+2 = 27 \text{ weeks.}\)

Show Worked Solution

a.    \(\text{The critical path is the continuous solid bar on row 1 of the Gantt chart.}\)

\(\text{Critical path:}\ ACDFGI\)
 

b.    \(\text{Activities B and H are not labelled in the network diagram.}\)

\(\text{From the Gantt chart:}\)

\(\text{B starts at week 0, ends at week 5} \to \text{duration} = 5 \text{ weeks}\)

\(\text{H starts at week 7, ends at week 14} \to \text{duration} = 7 \text{ weeks}\)
 

c.    \(\text{From the Gantt chart, activity E has a float of 6 weeks (see the dashed}\)

\(\text{extension from week 10 to 16).}\)

\(\text{The delay of 8 weeks exceeds the float of 6 weeks.}\)

\(\text{The project will be delayed by } 8-6 = 2 \text{ weeks.}\)

\(\text{New minimum completion time} = 25+2 = 27 \text{ weeks.}\)

Networks, STD2 N3 2023 HSC 31

A function centre employs staff so that all necessary tasks can be completed between the end of one function and the beginning of the next function.

The network diagram shows the time taken in hours for the tasks that need to be completed.
 


 

  1. Find the TWO critical paths.   (2 marks)

  2. The function centre wants to decrease the length of each critical path by 3 hours. They can do this by hiring more staff to do ONE of the tasks so it takes less time to complete.
  3. For which task should the centre hire more staff, and how long should that task take to ensure all tasks can be completed in 14 hours?   (2 marks) 

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a.    `HIGC and HIK`

b.    `text{More staff should be hired for task}\ I.`

`text{By decreasing task}\ I\ text{by 3 hours (so it takes 4 hours), the}`

`text{critical path of the network reduces to 14 hours.}`

Show Worked Solution

a.    `text{Scanning both ways:}`
 

`text{Critical paths:}\ HIGC and HIK`

♦ Mean mark (a) 46%.

 
b.    `text{More staff should be hired for task}\ I.`

`text{By decreasing task}\ I\ text{by 3 hours (so it takes 4 hours), the}`

`text{critical path of the network reduces to 14 hours.}`

Mean mark (b) 52%.

Networks, STD2 N3 2021 FUR1 6

The directed graph below shows the sequence of activities required to complete a project.

The time taken to complete each activity, in hours, is also shown.
 

The minimum completion time for this project is 18 hours.

The time taken to complete activity `E` is labelled  `x`.

What is the maximum value of  `x`?   (2 marks)

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`text(3 hours)`

Show Worked Solution

`text{Consider all possible network paths:}`

`ADHJ \ -> \ text{18 hours}`

`BEJ \ -> \ (12 + x) \ text{hours}`

`CGFEJ \ -> \  (15 + x) \ text{hours}`

`CGIJ \ -> \ text{18 hours}`
 

`text{Minimum completion time = 18 hours}`

`=>\ text{No path can be longer than 18 hours}`

`:. \ x_text{max} = 3 \ text{hours}`

Networks, STD2 N3 2014 FUR1 8 MC

Which one of the following statements about critical paths is true?

  1. There can be only one critical path in a project.
  2. A critical path will always include the activity that takes the longest time to complete.
  3. Reducing the time of any activity on a critical path for a project will always reduce the minimum completion time for the project.
  4. If there are no other changes, increasing the time of any activity on a critical path will always increase the completion time of a project.
Show Answers Only

`D`

Show Worked Solution

`text(If any activity on a critical path takes longer, the project)`

♦ Mean mark 40%.

`text{completion time increases by the equivalent amount}`

`text{of time (although the reverse is not true).}`

`=>  D`