Edexcel D1 2013 January — Question 7 16 marks

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2013
SessionJanuary
Marks16
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCritical Path Analysis
TypeExplain dummy activities
DifficultyEasy -1.2 This is a standard D1 critical path analysis question testing routine procedures: identifying dummy activities (straightforward concept recall), calculating early/late times, finding critical path, and drawing a Gantt chart. All parts follow textbook methods with no novel problem-solving required, making it easier than average A-level maths.
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 float

7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bd6edbd4-1ec0-4c7e-bd39-b88f96bf52fb-8_752_1445_210_287} \captionsetup{labelformat=empty} \caption{Figure 7}
\end{figure} Figure 7 is the activity network relating to a building project. The activities are represented by the arcs. The number in brackets on each arc gives the time to complete the activity. Each activity requires one worker. The project must be completed in the shortest possible time.
  1. Explain the reason for the dotted line from event 4 to event 6 as shown in Figure 7.
    (2)
  2. Complete Diagram 1 in the answer book to show the early event times and the late event times.
  3. State the critical activities.
  4. Calculate the total float for activity G. You must make the numbers you use in your calculation clear.
  5. Draw a Gantt chart for this project on the grid provided in the answer book.
  6. State the activities that must be happening at time 5.5
  7. Use your Gantt chart to determine the minimum number of workers needed to complete the project in the minimum time. You must justify your answer.

7.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{bd6edbd4-1ec0-4c7e-bd39-b88f96bf52fb-8_752_1445_210_287}
\captionsetup{labelformat=empty}
\caption{Figure 7}
\end{center}
\end{figure}

Figure 7 is the activity network relating to a building project. The activities are represented by the arcs. The number in brackets on each arc gives the time to complete the activity. Each activity requires one worker.

The project must be completed in the shortest possible time.
\begin{enumerate}[label=(\alph*)]
\item Explain the reason for the dotted line from event 4 to event 6 as shown in Figure 7.\\
(2)
\item Complete Diagram 1 in the answer book to show the early event times and the late event times.
\item State the critical activities.
\item Calculate the total float for activity G. You must make the numbers you use in your calculation clear.
\item Draw a Gantt chart for this project on the grid provided in the answer book.
\item State the activities that must be happening at time 5.5
\item Use your Gantt chart to determine the minimum number of workers needed to complete the project in the minimum time. You must justify your answer.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D1 2013 Q7 [16]}}