5 A firm is considering various strategies for development over the next few years. In the network, the number on each edge is the expected profit, in millions of pounds, moving from one year to the next. A negative number indicates a loss because of building costs or other expenses. Each path from \(S\) to \(T\) represents a complete strategy.
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1. By completing the table on the page opposite, or otherwise, use dynamic programming working backwards from \(\boldsymbol { T }\) to find the maximum weight of all paths from \(S\) to \(T\).
2. State the overall maximum profit and the paths from \(S\) to \(T\) corresponding to this maximum profit.

3. Stage	State	From	Calculation	Value
   1	G	\(T\)
   	H	\(T\)
   	I	\(T\)
   2	D	G
   		\(H\)
   	E	G
   		\(H\)
   		I
   	\(F\)	\(H\)
   		I
   3

4. Maximum profit is £ \(\_\_\_\_\) million Corresponding paths from \(S\) to \(T\) \(\_\_\_\_\)