| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matchings and Allocation |
| Type | Hungarian algorithm with unequal sets |
| Difficulty | Moderate -0.3 This is a standard textbook application of the Hungarian algorithm with minimal complexity. Part (i) requires adding a dummy row to make the matrix square, then mechanically applying the algorithm—a routine procedure for D2 students. Part (ii) simply involves removing one row and re-applying the same algorithm. The question tests procedural fluency rather than problem-solving or insight, making it slightly easier than average A-level maths questions overall. |
| Spec | 7.04a Shortest path: Dijkstra's algorithm |
| \multirow{7}{*}{Trainer} | \multirow{2}{*}{} | City | |||
| London | Glasgow | Manchester | Swansea | ||
| Adam | 4 | 3 | 2 | 4 | |
| Betty | 3 | 5 | 4 | 2 | |
| Clive | 3 | 6 | 3 | 3 | |
| Dave | 2 | 6 | 4 | 3 | |
| Eleanor | 2 | 5 | 3 | 4 | |
| Answer | Marks | Guidance |
|---|---|---|
| I appreciate your request, but the content you've provided appears to be incomplete or unclear. The text "2 | 0 | 0\n1 |
I appreciate your request, but the content you've provided appears to be incomplete or unclear. The text "2 | 0 | 0\n1 | 0\n2 | 0" doesn't appear to be a mark scheme with marking annotations (M1, A1, B1, etc.) or mathematical content that needs conversion to LaTeX.
Could you please provide the full extracted mark scheme content? Once you share the complete text with:
- The actual marking points
- The annotations (M1, A1, B1, DM1, etc.)
- Any mathematical symbols or notation that needs conversion
I'll be able to clean it up properly according to your specifications.2 A company has organised four regional training sessions to take place at the same time in four different cities. The company has to choose four of its five trainers, one to lead each session. The cost ( $\pounds 1000$ 's) of using each trainer in each city is given in the table.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
\multirow{7}{*}{Trainer} & \multirow{2}{*}{} & \multicolumn{4}{|c|}{City} \\
\hline
& & London & Glasgow & Manchester & Swansea \\
\hline
& Adam & 4 & 3 & 2 & 4 \\
\hline
& Betty & 3 & 5 & 4 & 2 \\
\hline
& Clive & 3 & 6 & 3 & 3 \\
\hline
& Dave & 2 & 6 & 4 & 3 \\
\hline
& Eleanor & 2 & 5 & 3 & 4 \\
\hline
\end{tabular}
\end{center}
(i) Convert this into a square matrix and then apply the Hungarian algorithm, reducing rows first, to allocate the trainers to the cities at minimum cost.\\
(ii) Betty discovers that she is not available on the date set for the training. Find the new minimum cost allocation of trainers to cities.
\hfill \mbox{\textit{OCR D2 Q2 [9]}}