| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2007 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate float times |
| Difficulty | Moderate -0.8 This is a standard D1 critical path analysis question requiring routine application of well-practiced algorithms: drawing an activity network, calculating early/late times, finding critical path, computing floats, and then optimizing with activity crashing. While multi-part with several steps, each component follows textbook procedures with no novel problem-solving required, making it easier than average A-level maths. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities7.05c Total float: calculation and interpretation |
| Activity | Duration (days) | Immediate predecessors | |
| A | Build concrete frame | 10 | \(-\) |
| B | Lay bricks | 7 | A |
| C | Lay roof tiles | 10 | A |
| D | First fit electrics | 5 | B |
| E | First fit plumbing | 4 | B |
| F | Plastering | 6 | C, D, E |
| G | Second fit electrics | 3 | F |
| H | Second fit plumbing | 2 | F |
| I | Tiling | 10 | G, H |
| J | Fit sanitary ware | 2 | H |
| K | Fit windows and doors | 5 | I |
| Answer | Marks | Guidance |
|---|---|---|
| Activity | Duration (days) | Immediate predecessors |
| A | Build concrete frame | 10 |
| B | Lay bricks | 7 |
| C | Lay roof tiles | 10 |
| D | First fit electrics | 5 |
| E | First fit plumbing | 4 |
| F | Plastering | 6 |
| G | Second fit electrics | 3 |
| H | Second fit plumbing | 2 |
| I | Tiling | 10 |
| J | Fit sanitary ware | 2 |
| K | Fit windows and doors | 5 |
Question 4:
4
Section B (48 marks)
4 Cassi is managing the building of a house. The table shows the major activities that are involved,
their durations and their precedences.
Activity Duration (days) Immediate predecessors
A Build concrete frame 10 –
B Lay bricks 7 A
C Lay roof tiles 10 A
D First fit electrics 5 B
E First fit plumbing 4 B
F Plastering 6 C, D, E
G Second fit electrics 3 F
H Second fit plumbing 2 F
I Tiling 10 G, H
J Fit sanitary ware 2 H
K Fit windows and doors 5 I
(i) Draw an activity-on-arc network to represent this information. [5]
(ii) Find the early time and the late time for each event. Give the project duration and list the
critical activities. [6]
(iii) Calculate total and independent floats for each non-critical activity. [2]
Cassi’s clients wish to take delivery in 42 days. Some durations can be reduced, at extra cost, to
achieve this.
• The tiler will finish activity I in 9 days for an extra £250, or in 8 days for an extra £500.
• The bricklayer will cut his total of 7 days on activity B by up to 3 days at an extra cost of £350
per day.
• The electrician could be paid £300 more to cut a day off activity D, or £600 more to cut two
days.
(iv) What is the cheapest way in which Cassi can get the house built in 42 days? [3]
Activity | Duration (days) | Immediate predecessors
A | Build concrete frame | 10 | –
B | Lay bricks | 7 | A
C | Lay roof tiles | 10 | A
D | First fit electrics | 5 | B
E | First fit plumbing | 4 | B
F | Plastering | 6 | C, D, E
G | Second fit electrics | 3 | F
H | Second fit plumbing | 2 | F
I | Tiling | 10 | G, H
J | Fit sanitary ware | 2 | H
K | Fit windows and doors | 5 | ICassi is managing the building of a house. The table shows the major activities that are involved, their durations and their precedences.
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
Activity & Duration (days) & Immediate predecessors \\
\hline
A & Build concrete frame & 10 & $-$ \\
\hline
B & Lay bricks & 7 & A \\
\hline
C & Lay roof tiles & 10 & A \\
\hline
D & First fit electrics & 5 & B \\
\hline
E & First fit plumbing & 4 & B \\
\hline
F & Plastering & 6 & C, D, E \\
\hline
G & Second fit electrics & 3 & F \\
\hline
H & Second fit plumbing & 2 & F \\
\hline
I & Tiling & 10 & G, H \\
\hline
J & Fit sanitary ware & 2 & H \\
\hline
K & Fit windows and doors & 5 & I \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\roman*)]
\item Draw an activity-on-arc network to represent this information. [5]
\item Find the early time and the late time for each event. Give the project duration and list the critical activities. [6]
\item Calculate total and independent floats for each non-critical activity. [2]
\end{enumerate}
Cassi's clients wish to take delivery in 42 days. Some durations can be reduced, at extra cost, to achieve this.
\begin{itemize}
\item The tiler will finish activity I in 9 days for an extra £250, or in 8 days for an extra £500.
\item The bricklayer will cut his total of 7 days on activity B by up to 3 days at an extra cost of £350 per day.
\item The electrician could be paid £300 more to cut a day off activity D, or £600 more to cut two days.
\end{itemize}
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{3}
\item What is the cheapest way in which Cassi can get the house built in 42 days? [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI D1 2007 Q4 [16]}}