2. The owner of a small plane is planning a journey from her local airport, \(A\) to the airport nearest her parents, \(K\). On the journey she will make three refuelling stops, the first at \(B , C\) or \(D\), the second at \(E , F\) or \(G\) and the third at \(H , I\) or \(J\).
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\includegraphics[alt={},max width=\textwidth]{34728928-2a21-463d-982e-c46ab2dc05c8-2_723_1303_427_356}
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\caption{Fig. 1}
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Figure 1 shows all the possible flights that can be made on the journey with the number by each arc indicating the distance of each flight in hundreds of miles. The owner of the plane wishes to choose a route that minimises the total distance that she flies.
Use dynamic programming to find the route that she should use and state the total length of this route.