| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 18 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Network Flows |
| Type | Transportation problem: stepping-stone method |
| Difficulty | Standard +0.3 This is a standard D2 transportation problem requiring mechanical application of the north-west corner rule and stepping-stone method. While the stepping-stone method involves multiple iterations and careful bookkeeping (hence 15 marks), it follows a well-defined algorithm with no conceptual insight required. The degeneracy identification is straightforward. This is slightly easier than average as it's purely algorithmic execution of taught procedures. |
| Spec | 7.04f Network problems: choosing appropriate algorithm |
| D | E | F | Supply | |
| A | 13 | 11 | 14 | 20 |
| B | 10 | 9 | 12 | 15 |
| C | 15 | 6 | 8 | 25 |
| Demand | 30 | 5 | 25 |
A transportation problem has costs, in pounds, and supply and demand, in appropriate units, as given in the transportation tableau below.
\begin{tabular}{c|ccc|c}
& D & E & F & Supply \\
\hline
A & 13 & 11 & 14 & 20 \\
B & 10 & 9 & 12 & 15 \\
C & 15 & 6 & 8 & 25 \\
\hline
Demand & 30 & 5 & 25 & \\
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Find the initial solution given by the north-west corner rule and state why it is degenerate. [3 marks]
\item Use the stepping-stone method to obtain an optimal solution minimising total cost. State the resulting transportation pattern and its total cost. [15 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 Q7 [18]}}