Edexcel D1 — Question 5

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
TopicCombinations & Selection

5. This question should be answered on the sheet provided. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{64203218-06e8-46f8-8aa9-7841ee2096c8-04_794_1315_280_296} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} In Figure 2 the weight on each arc represents the cost in pounds of translating a certain document between the two languages at the nodes that it joins. You may assume that the cost is the same for translating in either direction.
  1. Use Kruskal's algorithm to find the minimum cost of obtaining a translation of the document from English into each of the other languages on the network. You must show the order in which the arcs were selected.
    (4 marks)
  2. It is decided that a Greek translation is not needed. Find the minimum cost if:
    1. translations to and from Greek are not available,
    2. translations to and from Greek are still available.
  3. Comment on your findings. Another document is to be translated into 60 languages. It is now also necessary to take into account the fact that the cost of a translation between two languages depends on which language you start from.
  4. How would you overcome the problem of having different costs for reverse translations?
  5. What algorithm would be suitable to find a computerised solution.
  6. State another assumption you have made in answering this question and comment on its validity.
    (2 marks) \section*{6. This question should be answered on the sheet provided.} There are 5 computers in an office, each of which must be dedicated to a single application. The computers have different specifications and the following table shows which applications each computer is capable of running.
    ComputerApplications
    EAnimation
    FOffice, Data
    GSimulation
    HAnimation, Office
    IData, CAD, Simulation