Edexcel D1 2003 June — Question 5 15 marks

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2003
SessionJune
Marks15
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCritical Path Analysis
TypeCalculate lower bound for workers
DifficultyModerate -0.3 This is a standard Critical Path Analysis question covering routine D1 techniques: forward/backward pass, identifying critical path, calculating float, and basic scheduling. All parts follow textbook procedures with no novel problem-solving required, though part (e) requires careful application of the scheduling algorithm. Slightly easier than average due to the mechanical nature of CPA methods.
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

\includegraphics{figure_3} The network in Fig. 3 shows the activities involved in the process of producing a perfume. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, taken to complete the activity.
  1. Calculate the early time and the late time for each event, showing them on Diagram 1 in the answer booklet. [4]
  2. Hence determine the critical activities. [2]
  3. Calculate the total float time for \(D\). [2]
Each activity requires only one person.
  1. Find a lower bound for the number of workers needed to complete the process in the minimum time. [2]
Given that there are only three workers available, and that workers may not share an activity,
  1. schedule the activities so that the process is completed in the shortest time. Use the time line in the answer booklet. State the new shortest time. [5]

\includegraphics{figure_3}

The network in Fig. 3 shows the activities involved in the process of producing a perfume. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, taken to complete the activity.

\begin{enumerate}[label=(\alph*)]
\item Calculate the early time and the late time for each event, showing them on Diagram 1 in the answer booklet.
[4]
\item Hence determine the critical activities.
[2]
\item Calculate the total float time for $D$.
[2]
\end{enumerate}

Each activity requires only one person.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Find a lower bound for the number of workers needed to complete the process in the minimum time.
[2]
\end{enumerate}

Given that there are only three workers available, and that workers may not share an activity,

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{4}
\item schedule the activities so that the process is completed in the shortest time. Use the time line in the answer booklet. State the new shortest time.
[5]
\end{enumerate}

\hfill \mbox{\textit{Edexcel D1 2003 Q5 [15]}}