| Exam Board | AQA |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2015 |
| Session | June |
| Marks | 11 |
| 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 Hungarian algorithm application with a 5×4 matrix (unequal sets). While it requires careful execution through multiple steps (column reduction, row reduction, covering zeros, adjusting), it's a routine algorithmic procedure taught directly in D2 with no conceptual insight needed. The 11 marks reflect length rather than difficulty. Slightly easier than average due to being purely mechanical. |
| Spec | 7.01d Multiplicative principle: arrangements of n distinct objects |
| Leg 1 | Leg 2 | Leg 3 | Leg 4 | |
| Athlete \(\boldsymbol { A }\) | 9.84 | 8.91 | 8.98 | 8.70 |
| Athlete \(\boldsymbol { B }\) | 10.28 | 9.06 | 9.24 | 9.05 |
| Athlete \(\boldsymbol { C }\) | 10.31 | 9.11 | 9.22 | 9.18 |
| Athlete \(\boldsymbol { D }\) | 10.04 | 9.07 | 9.19 | 9.01 |
| Athlete \(\boldsymbol { E }\) | 9.91 | 8.95 | 9.09 | 8.74 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | 4 | 0 |
Question 3:
3 | 4 | 03 In the London 2012 Olympics, the Jamaican $4 \times 100$ metres relay team set a world record time of 36.84 seconds.
Athletes take different times to run each of the four legs.\\
The coach of a national athletics team has five athletes available for a major championship. The lowest times that the five athletes take to cover each of the four legs is given in the table below.
The coach is to allocate a different athlete from the five available athletes, $A , B , C , D$ and $E$, to each of the four legs to produce the lowest total time.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
& Leg 1 & Leg 2 & Leg 3 & Leg 4 \\
\hline
Athlete $\boldsymbol { A }$ & 9.84 & 8.91 & 8.98 & 8.70 \\
\hline
Athlete $\boldsymbol { B }$ & 10.28 & 9.06 & 9.24 & 9.05 \\
\hline
Athlete $\boldsymbol { C }$ & 10.31 & 9.11 & 9.22 & 9.18 \\
\hline
Athlete $\boldsymbol { D }$ & 10.04 & 9.07 & 9.19 & 9.01 \\
\hline
Athlete $\boldsymbol { E }$ & 9.91 & 8.95 & 9.09 & 8.74 \\
\hline
\end{tabular}
\end{center}
Use the Hungarian algorithm, by reducing the columns first, to assign an athlete to each leg so that the total time of the four athletes is minimised.
State the allocation of the athletes to the four legs and the total time.\\[0pt]
[11 marks]
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{b0f9523e-51dd-495f-99ec-4724243b5619-08_1200_1705_1507_155}
\end{center}
\hfill \mbox{\textit{AQA D2 2015 Q3 [11]}}