| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matchings and Allocation |
| Type | Transportation problem: stepping-stone method |
| Difficulty | Moderate -0.5 This is a standard textbook application of the stepping-stone method for transportation problems. While it requires multiple steps (north-west corner initial solution, then iterative improvement), the algorithm is mechanical and follows a prescribed procedure taught in D2. The 11 marks reflect length rather than conceptual difficulty—it's easier than average A-level maths as it requires no creative problem-solving, just careful execution of a learned algorithm. |
| Spec | 7.06a 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 |
| \(W _ { 1 }\) | \(W _ { 2 }\) | \(W _ { 3 }\) | Available | |
| \(S _ { 1 }\) | 12 | 11 | 17 | 30 |
| \(S _ { 2 }\) | 7 | 5 | 10 | 25 |
| \(S _ { 3 }\) | 5 | 6 | 8 | 10 |
| Required | 20 | 15 | 30 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| North-west corner solution: \(S_1W_1=20, S_1W_2=10, S_2W_2=5, S_2W_3=20, S_3W_3=10\) | M1A1 | |
| Shadow costs calculated correctly | M1A1 | |
| Improvement indices calculated, most negative identified | M1A1 | |
| Stepping stone path and reallocation correct | M1 | |
| Optimal solution stated with total cost | A1A1 |
# Question 4:
| Answer | Marks | Guidance |
|--------|-------|----------|
| North-west corner solution: $S_1W_1=20, S_1W_2=10, S_2W_2=5, S_2W_3=20, S_3W_3=10$ | M1A1 | |
| Shadow costs calculated correctly | M1A1 | |
| Improvement indices calculated, most negative identified | M1A1 | |
| Stepping stone path and reallocation correct | M1 | |
| Optimal solution stated with total cost | A1A1 | |
---4. A furniture manufacturer has three workshops, $W _ { 1 } , W _ { 2 }$ and $W _ { 3 }$. Orders for rolls of fabric are to be placed with three suppliers, $S _ { 1 } , S _ { 2 }$ and $S _ { 3 }$. The supply, demand and cost per roll in pounds, according to which supplier each workshop uses, are given in the table below.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
& $W _ { 1 }$ & $W _ { 2 }$ & $W _ { 3 }$ & Available \\
\hline
$S _ { 1 }$ & 12 & 11 & 17 & 30 \\
\hline
$S _ { 2 }$ & 7 & 5 & 10 & 25 \\
\hline
$S _ { 3 }$ & 5 & 6 & 8 & 10 \\
\hline
Required & 20 & 15 & 30 & \\
\hline
\end{tabular}
\end{center}
Starting with the north-west corner method of finding an initial solution, find an optimal transportation pattern which minimises the total cost. State the final solution and its total cost.\\
(11 marks)\\
\hfill \mbox{\textit{Edexcel D2 Q4 [11]}}