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
TypeDraw cascade/Gantt chart
DifficultyModerate -0.8 This is a standard D1 critical path analysis question requiring routine application of well-practiced algorithms (forward/backward pass, identifying critical path, drawing cascade chart). While multi-part with several marks, each step follows a mechanical procedure taught explicitly in the syllabus with no novel problem-solving or insight required.
Spec7.05a Critical path analysis: activity on arc networks7.05d Latest start and earliest finish: independent and interfering float
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4609ffb5-d270-4ff3-aa44-af8442a38b66-8_499_1319_191_383} \captionsetup{labelformat=empty} \caption{Figure 5}
\end{figure} A company models a project by the activity network shown in Figure 5. 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.
  1. Add early and late event times to Diagram 1 in the answer book.
  2. State the critical path and its length.
  3. On Diagram 2 in the answer book, construct a cascade (Gantt) chart.
  4. By using your cascade chart, state which activities must be happening at
    1. time 7.5
    2. time 16.5 It is decided that the company may use up to 25 days to complete the project.
  5. On Diagram 3 in the answer book, construct a scheduling diagram to show how this project can be completed within 25 days using as few workers as possible.
Question 7:
Part a
AnswerMarks Guidance
AnswerMark Guidance
All top boxes and all bottom boxes completed, values generally increasing left to right (top) and decreasing right to left (bottom)M1 Condone missing 0 or 22 for M only (bottom boxes); condone one rogue value in top boxes and one rogue in bottom boxes
CAO for top boxesA1
CAO for bottom boxesA1
Part b
AnswerMarks Guidance
AnswerMark Guidance
ADFJB1 CAO path
Length 22B1 CAO length
Part c
AnswerMarks Guidance
AnswerMark Guidance
At least 8 different activities including at least 4 floatsM1
Critical activities dealt with correctlyA1
The correct 11 activities (only once) including at least 7 floatsM1
Non-critical activities dealt with correctlyA1
Part d
AnswerMarks Guidance
AnswerMark Guidance
i) D & EB1 CAO
ii) J & GB1 CAO
Part e
AnswerMarks Guidance
AnswerMark Guidance
2 lines for 2 workers or 3 lines for 3 workers, all 11 activities present (just once) with time \(\leq 25\)M1
2 workers; condone one error either precedence or activity length; time must be 25A1 e.g. Worker 1: A(4), D(7), F(4), G(6), K(4); Worker 2: B(3), E(5), C(3), H(2), I(4), J(7)
2 workers; no errorsA1 
# Question 7:

## Part a
| Answer | Mark | Guidance |
|--------|------|----------|
| All top boxes and all bottom boxes completed, values generally increasing left to right (top) and decreasing right to left (bottom) | M1 | Condone missing 0 **or** 22 for M only (bottom boxes); condone one rogue value in top boxes **and** one rogue in bottom boxes |
| CAO for top boxes | A1 | |
| CAO for bottom boxes | A1 | |

## Part b
| Answer | Mark | Guidance |
|--------|------|----------|
| ADFJ | B1 | CAO path |
| Length 22 | B1 | CAO length |

## Part c
| Answer | Mark | Guidance |
|--------|------|----------|
| At least 8 different activities including at least 4 floats | M1 | |
| Critical activities dealt with correctly | A1 | |
| The correct 11 activities (only once) including at least 7 floats | M1 | |
| Non-critical activities dealt with correctly | A1 | |

## Part d
| Answer | Mark | Guidance |
|--------|------|----------|
| i) D & E | B1 | CAO |
| ii) J & G | B1 | CAO |

## Part e
| Answer | Mark | Guidance |
|--------|------|----------|
| 2 lines for 2 workers or 3 lines for 3 workers, all 11 activities present (just once) with time $\leq 25$ | M1 | |
| 2 workers; condone one error either precedence or activity length; time must be 25 | A1 | e.g. Worker 1: A(4), D(7), F(4), G(6), K(4); Worker 2: B(3), E(5), C(3), H(2), I(4), J(7) |
| 2 workers; no errors | A1 | |
7.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{4609ffb5-d270-4ff3-aa44-af8442a38b66-8_499_1319_191_383}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{center}
\end{figure}

A company models a project by the activity network shown in Figure 5. 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.
\begin{enumerate}[label=(\alph*)]
\item Add early and late event times to Diagram 1 in the answer book.
\item State the critical path and its length.
\item On Diagram 2 in the answer book, construct a cascade (Gantt) chart.
\item By using your cascade chart, state which activities must be happening at
\begin{enumerate}[label=(\roman*)]
\item time 7.5
\item time 16.5

It is decided that the company may use up to 25 days to complete the project.
\end{enumerate}\item On Diagram 3 in the answer book, construct a scheduling diagram to show how this project can be completed within 25 days using as few workers as possible.
\end{enumerate}

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