3 [Figure 1, printed on the insert, is provided for use in this question.]
The following network represents the footpaths connecting 12 buildings on a university campus. The number on each edge represents the time taken, in minutes, to walk along a footpath.
\includegraphics[max width=\textwidth, alt={}, center]{eb305e75-0e85-4f99-8f04-27046a153532-03_899_1317_589_356}

1. 1. Use Dijkstra's algorithm on Figure 1 to find the minimum time to walk from \(A\) to \(L\).
   2. State the corresponding route.
2. A new footpath is to be constructed. There are two possibilities:
   from \(A\) to \(D\), with a walking time of 30 minutes; or from \(A\) to \(I\), with a walking time of 20 minutes. Determine which of the two alternative new footpaths would reduce the walking time from \(A\) to \(L\) by the greater amount.
   (3 marks)