5 [Figure 3, printed on the insert, is provided for use in this question.]\\
A truck has to transport stones from a quarry, $Q$, to a builders yard, $Y$. The network shows the possible roads from $Q$ to $Y$. Along each road there are bridges with weight restrictions. The value on each edge indicates the maximum load in tonnes that can be carried by the truck along that particular road.\\
\includegraphics[max width=\textwidth, alt={}, center]{6c407dbf-efe5-49e4-881f-91e7de5c46d9-6_723_1280_589_372}

The truck is able to carry a load of up to 20 tonnes. The optimal route, known as the maximin route, is that for which the possible load that the truck can carry is as large as possible.
\begin{enumerate}[label=(\alph*)]
\item Explain why the route $Q A C Y$ is better than the route $Q B E Y$.
\item By completing the table on Figure 3, or otherwise, use dynamic programming, working backwards from $\boldsymbol { Y }$, to find the optimal (maximin) route from $Q$ to $Y$. Write down the maximin route and state the maximum possible load that the truck can carry from $Q$ to $Y$.
\end{enumerate}

\hfill \mbox{\textit{AQA D2 2009 Q5 [10]}}