4 The diagram shows a network of roads connecting 6 villages. The number on each edge is the length, in miles, of the road.
\includegraphics[max width=\textwidth, alt={}, center]{63e7775d-2a63-4584-b3be-ce97927bcfcc-04_670_1298_466_356} Total length of the roads \(= 164\) miles

1. A police patrol car based at village \(A\) has to travel along each road at least once before returning to \(A\). Find the length of an optimal 'Chinese postman' route for the police patrol car.
2. A council worker starts from \(A\) and travels along each road at least once before finishing at \(C\). Find the length of an optimal route for the council worker.
3. A politician is to travel along all the roads at least once. He can start his journey at any village and can finish his journey at any village.
   1. Find the length of an optimal route for the politician.
   2. State the vertices from which the politician could start in order to achieve this optimal route.