| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matchings and Allocation |
| Type | Transportation problem: stepping-stone method |
| Difficulty | Standard +0.3 This is a standard transportation problem using the north-west corner rule and stepping-stone method, which are algorithmic procedures taught in D2. The question requires following learned procedures rather than problem-solving insight, though it involves multiple steps. The small problem size (3×2 table) makes it more straightforward than typical examples. |
| Spec | 7.03l Bin packing: next-fit, first-fit, first-fit decreasing, full bin7.06a LP formulation: variables, constraints, objective function7.06b Slack variables: converting inequalities to equations7.06c Working with constraints: algebra and ad hoc methods7.06d Graphical solution: feasible region, two variables |
| \cline { 2 - 3 } \multicolumn{1}{c|}{} | \(A\) | \(B\) |
| \(C\) | 2 | 3 |
| \(D\) | 2 | 5 |
| \(E\) | 7 | 6 |
| Stage | State | Action | |||||
| \multirow[t]{2}{*}{1} | G | GI | |||||
| H | HI | ||||||
| \multirow[t]{3}{*}{2} | D |
| |||||
| E |
| ||||||
| F |
| ||||||
| \multirow[t]{3}{*}{3} | A |
| |||||
| B |
| ||||||
| C |
| ||||||
| 4 | Home |
|
7. Mrs. Hartley organises the tennis fixtures for her school. On one day she has to send a team of 10 players to a match against school $A$ and a team of 6 players to a match against school $B$. She has to select the two teams from a squad that includes 7 players who live in village $C$, 5 players who live in village $D$ and 8 players who live in village $E$.
Having a small budget, Mrs. Hartley wishes to minimise the total amount spent on travel. The table below shows the cost, in pounds, for one player to travel from each village to each of the schools they are competing against.
\begin{center}
\begin{tabular}{ | c | c | c | }
\cline { 2 - 3 }
\multicolumn{1}{c|}{} & $A$ & $B$ \\
\hline
$C$ & 2 & 3 \\
\hline
$D$ & 2 & 5 \\
\hline
$E$ & 7 & 6 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Use the north-west corner rule to find an initial solution to this problem.
\item Obtain improvement indices for this initial solution.
\item Use the stepping-stone method to obtain an optimal solution and state the pattern of transportation that this represents.
\section*{Please hand this sheet in for marking}
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
Stage & State & Action & & \\
\hline
\multirow[t]{2}{*}{1} & G & GI & & \\
\hline
& H & HI & & \\
\hline
\multirow[t]{3}{*}{2} & D & \begin{tabular}{l}
DG \\
DH \\
\end{tabular} & & \\
\hline
& E & \begin{tabular}{l}
EG \\
$E H$ \\
\end{tabular} & & \\
\hline
& F & \begin{tabular}{l}
FG \\
FH \\
\end{tabular} & & \\
\hline
\multirow[t]{3}{*}{3} & A & \begin{tabular}{l}
AD \\
$A E$ \\
$A F$ \\
\end{tabular} & & \\
\hline
& B & \begin{tabular}{l}
BD \\
BE \\
$B F$ \\
\end{tabular} & & \\
\hline
& C & \begin{tabular}{l}
CD \\
CE \\
CF \\
\end{tabular} & & \\
\hline
4 & Home & \begin{tabular}{l}
Home-A \\
Home-B \\
Home-C \\
\end{tabular} & & \\
\hline
\end{tabular}
\end{center}
\section*{Please hand this sheet in for marking}
(a)\\
\includegraphics[max width=\textwidth, alt={}, center]{4e50371b-0c1c-4b4e-b21d-60858ae160df-8_662_1025_529_440}\\
(b)
Sheet for answering question 6 (cont.)\\
(c)
\item \end{enumerate}
\hfill \mbox{\textit{Edexcel D2 Q7 [16]}}