Moderate -0.5 This is a standard algorithmic application of the north-west corner method and stepping-stone algorithm from Decision Mathematics. While it requires careful bookkeeping across multiple steps, it involves direct application of prescribed procedures with no problem-solving insight or novel reasoning required. The mechanical nature and routine application place it slightly below average difficulty.
Freezy Co. has three factories \(A , B\) and \(C\). It supplies freezers to three shops \(D , E\) and \(F\). The table shows the transportation cost in pounds of moving one freezer from each factory to each outlet. It also shows the number of freezers available for delivery at each factory and the number of freezers required at each shop. The total number of freezers required is equal to the total number of freezers available.
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\(D\)
\(E\)
\(F\)
Available
\(A\)
21
24
16
24
\(B\)
18
23
17
32
\(C\)
15
19
25
14
Required
20
30
20
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Use the north-west corner rule to find an initial solution.
Obtain improvement indices for each unused route.
Use the stepping-stone method once to obtain a better solution and state its cost.
\begin{enumerate}
\item Freezy Co. has three factories $A , B$ and $C$. It supplies freezers to three shops $D , E$ and $F$. The table shows the transportation cost in pounds of moving one freezer from each factory to each outlet. It also shows the number of freezers available for delivery at each factory and the number of freezers required at each shop. The total number of freezers required is equal to the total number of freezers available.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
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\multicolumn{1}{c|}{} & $D$ & $E$ & $F$ & Available \\
\hline
$A$ & 21 & 24 & 16 & 24 \\
\hline
$B$ & 18 & 23 & 17 & 32 \\
\hline
$C$ & 15 & 19 & 25 & 14 \\
\hline
Required & 20 & 30 & 20 & \multicolumn{1}{c}{} \\
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& & & & \\
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\end{tabular}
\end{center}
(a) Use the north-west corner rule to find an initial solution.\\
(b) Obtain improvement indices for each unused route.\\
(c) Use the stepping-stone method once to obtain a better solution and state its cost.\\
\hfill \mbox{\textit{Edexcel D2 2005 Q1 [11]}}