OCR MEI D1 2008 June — Question 5

Exam BoardOCR MEI
ModuleD1 (Decision Mathematics 1)
Year2008
SessionJune
TopicCritical Path Analysis

5
  1. The graphs below illustrate the precedences involved in running two projects, each consisting of the same activities \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D }\) and E . \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Project 1} \includegraphics[alt={},max width=\textwidth]{8eba759f-38bc-4d14-ac65-9a0ee6c79741-6_280_385_429_495}
    \end{figure} \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Project 2} \includegraphics[alt={},max width=\textwidth]{8eba759f-38bc-4d14-ac65-9a0ee6c79741-6_255_392_429_1187}
    \end{figure}
    1. For one activity the precedences in the two projects are different. State which activity and describe the difference.
    2. The table below shows the durations of the five activities.
      ActivityABCDE
      Duration21\(x\)32
      Give the total time for project 1 for all possible values of \(x\).
      Give the total time for project 2 for all possible values of \(x\).
  2. The durations and precedences for the activities in a project are shown in the table.
    ActivityDurationImmediate predecessors
    R2-
    S1-
    T5-
    w3R, S
    X2R, S, T
    Y3R
    Z1W, Y
    1. Draw an activity on arc network to represent this information.
    2. Find the early time and the late time for each event. Give the project duration and list the critical activities.