Practical modelling questions

A question is this type if and only if it asks to describe a practical problem that could be modelled by a given network or to critique/improve a network model.

2 questions · Moderate -0.4

7.04a Shortest path: Dijkstra's algorithm
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OCR MEI D1 2009 January Q3
8 marks Moderate -0.5
3 Whilst waiting for her meal to be served, Alice tries to construct a network to represent the meals offered in the restaurant. \includegraphics[max width=\textwidth, alt={}, center]{9bb2d545-3764-4930-a8a8-9dc5e25d0836-3_684_1310_365_379}
  1. Use Dijkstra's algorithm to find the cheapest route through the undirected network from "start" to "end". Give the cost and describe the route. Use the lettering given on the network in your answer book.
  2. Criticise the model and suggest how it might be improved.
Edexcel D1 Q5
12 marks Moderate -0.3
5. This question should be answered on the sheet provided. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6c6b7934-ab46-4a87-8a11-f99bf9a5d743-05_834_1436_306_280} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure} Figure 3 shows a weighted network. The number on each arc indicates the weight of that arc.
  1. Use Dijkstra's algorithm to find a path of least weight from \(A\) to \(J\) and state the weight of the path. Your solution must show clearly how you have applied the algorithm including:
    1. the order in which the vertices were labelled,
    2. how you determined the path of least weight.
  2. Find if there are any other paths of least weight and explain your answer.
  3. Describe a practical problem that could be modelled by the above network.