2. Table 1 shows the cost, in pounds, of transporting one unit of stock from each of three supply points, $\mathrm { A } , \mathrm { B }$ and C , to each of 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}{|l|l|l|l|l|l|}
\hline
 & 1 & 2 & 3 & 4 & Supply \\
\hline
A & 17 & 20 & 23 & 14 & 25 \\
\hline
B & 16 & 15 & 19 & 22 & 29 \\
\hline
C & 19 & 14 & 11 & 15 & 32 \\
\hline
Demand & 28 & 17 & 23 & 18 &  \\
\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.

\begin{table}[h]
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
 & 1 & 2 & 3 & 4 \\
\hline
$A$ & 25 &  &  &  \\
\hline
$B$ & 3 & 17 & 9 &  \\
\hline
$C$ &  &  & 14 & 18 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 2}
\end{center}
\end{table}
\begin{enumerate}[label=(\alph*)]
\item Taking A4 as the entering cell, use the stepping-stone method to find an improved solution. Make your route clear.
\item Taking the most negative improvement index to indicate the entering cell, use the stepping-stone method once to obtain an improved solution. You must make your method clear by stating your shadow costs, improvement indices, route, entering cell and exiting cell.
\item Determine whether your current solution is optimal, giving a reason for your answer.
\item State the cost of your current solution.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D2 2019 Q2 [10]}}