Edexcel D1 2014 June — Question 7 14 marks

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2014
SessionJune
Marks14
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCritical Path Analysis
TypeCalculate lower bound for workers
DifficultyModerate -0.5 This is a standard critical path analysis question covering routine D1 techniques: defining total float, finding early/late times, identifying critical activities, calculating float for a specific activity, and determining the lower bound for workers. All parts follow textbook procedures with no novel problem-solving required, though part (e) requires understanding that lower bound = total activity time รท project duration, which is slightly less routine than parts (b)-(d).
Spec7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities7.05c Total float: calculation and interpretation7.05d Latest start and earliest finish: independent and interfering float7.05e Cascade charts: scheduling and effect of delays
7. (a) In the context of critical path analysis, define the term 'total float'. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{818ba207-5839-4698-aacb-75dab88b218f-08_1310_1563_340_251} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 is the activity network for a building project. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the activity. Each activity requires exactly one worker. The project is to be completed in the shortest possible time.
(b) Complete Diagram 1 in the answer book to show the early event times and the late event times.
(c) State the critical activities.
(d) Calculate the maximum number of days by which activity G could be delayed without affecting the shortest possible completion time of the project. You must make the numbers used in your calculation clear.
(e) Calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working. The project is to be completed in the minimum time using as few workers as possible.
(f) Schedule the activities using Grid 1 in the answer book.
7. (a) In the context of critical path analysis, define the term 'total float'.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{818ba207-5839-4698-aacb-75dab88b218f-08_1310_1563_340_251}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

Figure 3 is the activity network for a building project. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the activity. Each activity requires exactly one worker. The project is to be completed in the shortest possible time.\\
(b) Complete Diagram 1 in the answer book to show the early event times and the late event times.\\
(c) State the critical activities.\\
(d) Calculate the maximum number of days by which activity G could be delayed without affecting the shortest possible completion time of the project. You must make the numbers used in your calculation clear.\\
(e) Calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working.

The project is to be completed in the minimum time using as few workers as possible.\\
(f) Schedule the activities using Grid 1 in the answer book.\\

\hfill \mbox{\textit{Edexcel D1 2014 Q7 [14]}}
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