| Exam Board | Edexcel |
|---|---|
| Module | FD2 (Further Decision 2) |
| Session | Specimen |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matchings and Allocation |
| Type | Transportation problem: stepping-stone method |
| Difficulty | Challenging +1.2 This is a standard algorithmic transportation problem requiring mechanical application of the north-west corner method followed by the stepping-stone algorithm. While it involves multiple iterations and careful bookkeeping, it requires no problem-solving insight or novel thinking—just systematic execution of a taught procedure from Further Decision 2, making it moderately above average difficulty primarily due to computational length rather than conceptual challenge. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06b Slack variables: converting inequalities to equations7.06c Working with constraints: algebra and ad hoc methods |
| D | E | F | Available | |
| A | 15 | 19 | 9 | 25 |
| B | 11 | 18 | 10 | 55 |
| C | 11 | 12 | 18 | 20 |
| Required | 38 | 24 | 38 |
2.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
& D & E & F & Available \\
\hline
A & 15 & 19 & 9 & 25 \\
\hline
B & 11 & 18 & 10 & 55 \\
\hline
C & 11 & 12 & 18 & 20 \\
\hline
Required & 38 & 24 & 38 & \\
\hline
\end{tabular}
\end{center}
A company has three factories, $\mathrm { A } , \mathrm { B }$ and C . It supplies mattresses to three shops, $\mathrm { D } , \mathrm { E }$ and F . The table shows the transportation cost, in pounds, of moving one mattress from each factory to each shop. It also shows the number of mattresses available at each factory and the number of mattresses required at each shop. A minimum cost solution is required.
\begin{enumerate}[label=(\alph*)]
\item Use the north-west corner method to obtain an initial solution.
\item Show how the transportation algorithm is used to solve this problem.
You must state, at each appropriate step, the
\begin{itemize}
\item shadow costs,
\item improvement indices,
\item route,
\item entering cell and exiting cell,\\
and explain clearly how you know that your final solution is optimal.
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{Edexcel FD2 Q2 [12]}}