5 [Figure 2, printed on the insert, is provided for use in this question.]
A company has a number of stores. The following network shows the possible actions and profits over the next five years. The number on each edge is the expected profit, in millions of pounds. A negative number indicates a loss due to investment in new stores.
\includegraphics[max width=\textwidth, alt={}, center]{1bf0d8b7-9f91-437a-bc18-3bfe5ca12223-06_1006_1583_591_223}

1. Working backwards from \(\boldsymbol { T }\), use dynamic programming to maximise the expected profits over the five years. You may wish to complete the table on Figure 2 as your solution.
2. State the maximum expected profit and the sequence of vertices from \(S\) to \(T\) in order to achieve this.
   (2 marks)