7 [Figure 2, printed on the insert, is provided for use in this question.]
The following network has eight vertices, \(A , B , \ldots , H\), and edges connecting some pairs of vertices. The number on each edge is its weight. The weights on the edges \(E H\) and \(G H\) are functions of \(x\) and \(y\).
\includegraphics[max width=\textwidth, alt={}, center]{4c5c963b-0183-4dc7-9054-b2c7a3eb8c1b-07_1170_1705_596_164} Given that there are three routes from \(A\) to \(H\) with the same minimum weight, use Dijkstra's algorithm on Figure 2 to find:

1. this minimum weight;
2. the values of \(x\) and \(y\).