3. Table 1 below shows the cost, in pounds, of transporting one unit of stock from each of four supply points, $\mathrm { A } , \mathrm { B } , \mathrm { C }$ and D , to four demand points $1,2,3$ and 4 . It also shows the stock held at each supply point and the stock required at each demand point. A minimum cost solution is required.

\begin{table}[h]
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
 & 1 & 2 & 3 & 4 & Supply \\
\hline
A & 22 & 36 & 19 & 37 & 35 \\
\hline
B & 29 & 35 & 30 & 36 & 15 \\
\hline
C & 24 & 32 & 25 & 41 & 20 \\
\hline
D & 23 & 30 & 23 & 38 & 30 \\
\hline
Demand & 30 & 20 & 30 & 20 &  \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{center}
\end{table}

Table 2 shows an initial solution given by the north-west corner method.\\
Table 3 shows some of the improvement indices for this solution.

\begin{table}[h]
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
 & 1 & 2 & 3 & 4 \\
\hline
A & 30 & 5 &  &  \\
\hline
B &  & 15 & 0 &  \\
\hline
C &  &  & 20 &  \\
\hline
D &  &  & 10 & 20 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 2}
\end{center}
\end{table}

\begin{table}[h]
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
 & 1 & 2 & 3 & 4 \\
\hline
A & x & x &  &  \\
\hline
B &  & x & x &  \\
\hline
C & 8 & 2 & x & 1 \\
\hline
D & 9 & 2 & x & x \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 3}
\end{center}
\end{table}
\begin{enumerate}[label=(\alph*)]
\item Explain why a zero has been placed in cell B3 in Table 2.\\
(1)
\item Calculate the shadow costs and the missing improvement indices and enter them into Table 3 in your answer book.
\item Taking the most negative improvement index to indicate the entering cell, state the steppingstone route that should be used to obtain the next solution. You must state your entering cell and exiting cell.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D2 2013 Q3 [8]}}