6 The network below has 11 vertices and 16 edges connecting some pairs of vertices. The numbers on the edges are their weights. The weight of the edge \(D G\) is given in terms of \(x\). There are three routes from \(A\) to \(K\) that have the same minimum total weight.
\includegraphics[max width=\textwidth, alt={}, center]{c2b62fee-d320-4701-a5bb-b2e4b8cc0952-16_863_1444_552_299} Working backwards from \(\boldsymbol { K }\), use dynamic programming, to find:

1. the minimum total weight from \(A\) to \(K\);
2. the value of \(x\);
3. the three routes corresponding to the minimum total weight. You must complete the table opposite as your solution.
   [0pt] [12 marks] \section*{Answer space for question 6}

   Stage	State	From	Calculation	Value
   1	I	K
   	\(J\)	K