Question 1 (4 marks)A council is constructing a new playground. This project involves completing tasks A to H. The varioustasks and their prerequisites are shown in the precedence table below.Task Time (weeks) Prerequisites Earliest start time Latest start timeA 2 None 0 0B 1 None 0 3C 1 A 2 2D 5 A and B 2 4E 3 C 3 4F 2 C 3 3G 2 E 6 7H 4 F 5 5Use the information in the table above to answer parts (a) to (d).(a) State the task that takes the longest time to complete.(1 mark)(b) List all of the tasks that must be completed on time in order to cause no delay.(1 mark)(c) Calculate the minimum completion time for the construction of the playground.(1 mark)(d) If a network diagram were to be drawn for this project, which task would require a dummy linkleading into it? Tick the appropriate box to indicate your answer.Task A Task D Task E Task G (1 mark)
Question
Question 1 (4 marks)A council is constructing a new playground. This project involves completing tasks A to H. The varioustasks and their prerequisites are shown in the precedence table below.Task Time (weeks) Prerequisites Earliest start time Latest start timeA 2 None 0 0B 1 None 0 3C 1 A 2 2D 5 A and B 2 4E 3 C 3 4F 2 C 3 3G 2 E 6 7H 4 F 5 5Use the information in the table above to answer parts (a) to (d).(a) State the task that takes the longest time to complete.(1 mark)(b) List all of the tasks that must be completed on time in order to cause no delay.(1 mark)(c) Calculate the minimum completion time for the construction of the playground.(1 mark)(d) If a network diagram were to be drawn for this project, which task would require a dummy linkleading into it? Tick the appropriate box to indicate your answer.Task A Task D Task E Task G (1 mark)
Solution
(a) The task that takes the longest time to complete is Task D, which takes 5 weeks.
(b) The tasks that must be completed on time in order to cause no delay are Tasks A, B, C, D, E, F, and H. This is because any delay in these tasks will push back the earliest start time of the tasks that depend on them.
(c) The minimum completion time for the construction of the playground can be calculated by adding up the time it takes to complete each task in the longest path through the project. This is known as the critical path. In this case, the critical path is A-C-E-G-H, which takes 2 (A) + 1 (C) + 3 (E) + 2 (G) + 4 (H) = 12 weeks.
(d) If a network diagram were to be drawn for this project, Task D would require a dummy link leading into it. This is because it has two prerequisites (Tasks A and B), and in a network diagram, a dummy link is used to show that a task cannot start until more than one other task has been completed.
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