AQA D2 2016 June — Question 1 12 marks

Exam BoardAQA
ModuleD2 (Decision Mathematics 2)
Year2016
SessionJune
Marks12
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCritical Path Analysis
TypeSchedule with limited workers - determine minimum time
DifficultyModerate -0.5 This is a standard Critical Path Analysis question covering routine D2 techniques: forward/backward pass, identifying critical path and float, drawing resource histograms, and scheduling with limited workers. While multi-part with several marks, all parts follow textbook algorithms with no novel problem-solving required, making it slightly easier than average A-level difficulty.
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

1
Figure 1 below shows an activity diagram for a project. Each activity requires one worker. The duration required for each activity is given in hours.
  1. Find the earliest start time and the latest finish time for each activity and insert these values on Figure 1.
    1. Find the critical path.
    2. Find the float time of activity \(F\).
  2. Using Figure 2 on page 3, draw a resource histogram to illustrate how the project can be completed in the minimum time, assuming that each activity is to start as early as possible.
    1. Given that there are two workers available for the project, find the minimum completion time for the project.
    2. Write down an allocation of tasks to the two workers that corresponds to your answer in part (d)(i). \section*{Answer space for question 1} \begin{figure}[h]
      \captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{34de3f03-a275-44fb-88b2-b88038bcec97-02_687_1655_1941_189}
      \end{figure} \section*{Answer space for question 1} \begin{figure}[h]
      \captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{34de3f03-a275-44fb-88b2-b88038bcec97-03_1115_1575_434_283}
      \end{figure}
      \includegraphics[max width=\textwidth, alt={}]{34de3f03-a275-44fb-88b2-b88038bcec97-03_1024_1593_1683_267}

AnswerMarks Guidance
AnswerMarks Guidance
Early times correct at \(E, F, H\) and \(I\)M1
All correctA1
Late times correct at \(I, H, F\) and \(E\) fit their answer to part (a)M1
All correctA1
CGIKLB1
2B1
SCA, resource histogram, at least 10 labelled activities shown, condone floats.M1
Two 'complete' horizontal rows, but no 'vertical gaps', showing correct progression, correct start times, (condone floats).A1
All correct (no floats) oeA1
\(A, B, D\) must be allocated to 1 worker leading to an answer \(63 \le x < (58+11)\) 63M1, A1 PI by part (ii)
\((A, B, D, E), (H, J), L\) and \((C, F, G), (I, K), (L)\)B1 \(\{A, B\}, D, E\) together and \(C, \{F, G\}\) together, then \(H, J\) together and \(I, K\) together
| Answer | Marks | Guidance |
|--------|-------|----------|
| Early times correct at $E, F, H$ and $I$ | M1 | |
| All correct | A1 | |
| Late times correct at $I, H, F$ and $E$ fit their answer to part (a) | M1 | |
| All correct | A1 | |
| CGIKL | B1 | |
| 2 | B1 | |
| SCA, resource histogram, at least 10 labelled activities shown, condone floats. | M1 | |
| Two 'complete' horizontal rows, but no 'vertical gaps', showing correct progression, correct start times, (condone floats). | A1 | |
| All correct (no floats) oe | A1 | |
| $A, B, D$ must be allocated to 1 worker leading to an answer $63 \le x < (58+11)$ 63 | M1, A1 | PI by part (ii) |
| $(A, B, D, E), (H, J), L$ and $(C, F, G), (I, K), (L)$ | B1 | $\{A, B\}, D, E$ together and $C, \{F, G\}$ together, then $H, J$ together and $I, K$ together |
1\\
Figure 1 below shows an activity diagram for a project. Each activity requires one worker. The duration required for each activity is given in hours.
\begin{enumerate}[label=(\alph*)]
\item Find the earliest start time and the latest finish time for each activity and insert these values on Figure 1.
\item \begin{enumerate}[label=(\roman*)]
\item Find the critical path.
\item Find the float time of activity $F$.
\end{enumerate}\item Using Figure 2 on page 3, draw a resource histogram to illustrate how the project can be completed in the minimum time, assuming that each activity is to start as early as possible.
\item \begin{enumerate}[label=(\roman*)]
\item Given that there are two workers available for the project, find the minimum completion time for the project.
\item Write down an allocation of tasks to the two workers that corresponds to your answer in part (d)(i).

\section*{Answer space for question 1}
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
  \includegraphics[alt={},max width=\textwidth]{34de3f03-a275-44fb-88b2-b88038bcec97-02_687_1655_1941_189}
\end{center}
\end{figure}

\section*{Answer space for question 1}
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 2}
  \includegraphics[alt={},max width=\textwidth]{34de3f03-a275-44fb-88b2-b88038bcec97-03_1115_1575_434_283}
\end{center}
\end{figure}

\begin{center}
\includegraphics[max width=\textwidth, alt={}]{34de3f03-a275-44fb-88b2-b88038bcec97-03_1024_1593_1683_267}
\end{center}
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{AQA D2 2016 Q1 [12]}}