| Exam Board | AQA |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Dynamic programming shortest/longest path |
| Difficulty | Standard +0.3 This is a standard dynamic programming question requiring backward induction through a network to find the maximum profit path. While it involves multiple stages and careful bookkeeping, it follows a routine algorithmic procedure taught directly in D2 with no novel problem-solving required. The presence of negative values adds minimal complexity. Slightly easier than average due to its mechanical nature. |
| Spec | 7.03h Best/worst/typical case: run-time analysis |
| Answer | Marks | Guidance |
|---|---|---|
| I appreciate you sharing this content, but what you've provided appears to be only a header or reference row (5 | 2 | 3 |
I appreciate you sharing this content, but what you've provided appears to be only a header or reference row (5 | 2 | 3 | 0 | 6) rather than actual mark scheme content with marking annotations.
To clean up extracted mark scheme content properly, I would need the actual marking points, criteria, and annotations (M1, A1, B1, DM1, etc.).
Could you please provide the full mark scheme content for Question 5?5 [Figure 2, printed on the insert, is provided for use in this question.]\\
A company has a number of stores. The following network shows the possible actions and profits over the next five years. The number on each edge is the expected profit, in millions of pounds. A negative number indicates a loss due to investment in new stores.\\
\includegraphics[max width=\textwidth, alt={}, center]{1bf0d8b7-9f91-437a-bc18-3bfe5ca12223-06_1006_1583_591_223}
\begin{enumerate}[label=(\alph*)]
\item Working backwards from $\boldsymbol { T }$, use dynamic programming to maximise the expected profits over the five years. You may wish to complete the table on Figure 2 as your solution.
\item State the maximum expected profit and the sequence of vertices from $S$ to $T$ in order to achieve this.\\
(2 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA D2 2009 Q5 [9]}}