3. The table below shows the cost, in pounds, of transporting one unit of stock from each of four supply points, $\mathrm { E } , \mathrm { F } , \mathrm { G }$ and H , to three sales points, $\mathrm { A } , \mathrm { B }$ and C . It also shows the stock held at each supply point and the amount required at each sales point.\\
A minimum cost solution is required.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
 & A & B & C & Supply \\
\hline
E & 23 & 28 & 22 & 21 \\
\hline
F & 26 & 19 & 29 & 32 \\
\hline
G & 29 & 24 & 20 & 29 \\
\hline
H & 24 & 26 & 19 & 23 \\
\hline
Demand & 45 & 19 & 23 &  \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Explain why it is necessary to add a dummy demand point.
\item On Table 1 in the answer book, insert appropriate values in the dummy demand column, D.

After finding an initial feasible solution and applying one iteration of the stepping-stone method, the table becomes

\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
 & $A$ & $B$ & $C$ & $D$ \\
\hline
$E$ & 21 &  &  &  \\
\hline
$F$ & 19 & 13 &  &  \\
\hline
$G$ &  & 6 & 23 &  \\
\hline
$H$ & 5 &  &  & 18 \\
\hline
\end{tabular}
\end{center}
\item Starting with GD as the next entering cell, perform two further iterations of the stepping-stone method to obtain an improved solution. You must make your method clear by showing your routes and stating the

\begin{itemize}
  \item shadow costs
  \item improvement indices
  \item entering and exiting cells
\item State the cost of the solution found in (c).
\item Determine whether the solution obtained in (c) is optimal, giving a reason for your answer.
\end{itemize}
\end{enumerate}

\hfill \mbox{\textit{Edexcel FD2 2024 Q3 [12]}}