5 The arcs in the network below represent the tracks in a forest and the weights on the arcs represent distances in km.
\includegraphics[max width=\textwidth, alt={}, center]{cec8d4db-4a72-43a3-88f3-ff9df2a11d2c-6_543_1269_392_438} Dijkstra's algorithm is to be used to find the shortest path from \(A\) to \(G\).

1. Apply Dijkstra's algorithm to find the shortest path from \(A\) to \(G\). Show your working, including temporary labels, permanent labels and the order in which permanent labels are assigned. Do not cross out your working values. Write down the route of the shortest path from \(A\) to \(G\) and give its length. The track joining \(B\) and \(D\) is washed away in a flood. It is replaced by a new track of unknown length, \(x \mathrm {~km}\).
   \includegraphics[max width=\textwidth, alt={}, center]{cec8d4db-4a72-43a3-88f3-ff9df2a11d2c-6_544_1271_1480_438}
2. What is the smallest value that \(x\) can take so that the route found in part (i) is still a shortest path? If the value of \(x\) is smaller than this, what is the weight of the shortest path from \(A\) to \(G\) ?
3. (a) For what values of \(x\) will vertex \(E\) have two temporary labels? Write down the values of these temporary labels.
   (b) For what values of \(x\) will vertex \(C\) have two temporary labels? Write down the values of these temporary labels. Dijkstra's algorithm has quadratic order.
4. If a computer takes 20 seconds to apply Dijkstra's algorithm to a complete network with 50 vertices, approximately how long will it take for a complete network with 100 vertices?