\includegraphics{figure_2}

A company has 3 warehouses $W_1$, $W_2$ and $W_3$. It needs to transport the goods stored there to 2 retail outlets $R_1$ and $R_2$. The capacities of the possible routes, in van loads per day, are shown in Fig. 2. Warehouses $W_1$, $W_2$ and $W_3$ have 14, 12 and 14 van loads respectively available per day and retail outlets $R_1$ and $R_2$ can accept 6 and 25 van loads respectively per day.

\begin{enumerate}[label=(\alph*)]
\item On Diagram 1 on the answer sheet add a supersource $W$ and a supersink $R$ and the appropriate directed arcs to obtain a single-source, single-sink capacitated network. State the minimum capacity of each arc you have added. [3]

\item State the maximum flow along
\begin{enumerate}[label=(\roman*)]
\item $W_1W_1R_1R$,
\item $W_2CR_2R$.
\end{enumerate} [2]

\item Taking your answers to part (b) as the initial flow pattern, use the labelling procedure to obtain a maximum flow through the network from $W$ to $R$. Show your working on Diagram 2. List each flow-augmenting route you find together with its flow. [5]

\item From your final flow pattern, determine the number of van loads passing through $B$ each day. [1]
\end{enumerate}

\hfill \mbox{\textit{Edexcel D2  Q12 [11]}}