| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Dynamic programming shortest/longest path |
| Difficulty | Moderate -0.5 This is a standard textbook dynamic programming problem with a small network (4 stages, clearly defined states). It requires systematic application of the DP algorithm working backwards through stages, but involves no conceptual challenges or novel problem-solving—just methodical calculation and bookkeeping. Slightly easier than average due to its routine nature and small problem size. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities |
I cannot provide a cleaned mark scheme from this content. The document you've shared appears to be an answer sheet template for students rather than a mark scheme. It contains:
- A diagram with nodes (A, B, C, D, E, F) and numerical values on edges
- Blank spaces for student answers in parts (a), (b), (c), and (d)
- No marking annotations (M1, A1, B1, DM1, etc.)
- No marking guidance or criteria
To clean up a mark scheme, I would need the actual mark scheme document that shows the correct solutions, marking points, and allocation of marks. Please provide the mark scheme content and I'll be happy to format it as requested.4. This question should be answered on the sheet provided.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{4e50371b-0c1c-4b4e-b21d-60858ae160df-3_771_1479_1178_237}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}
A salesman is planning a four-day trip beginning at home and ending at town $I$. He will spend the first night in town $A , B$ or $C$, the second night in town $D , E$ or $F$ and the third night in town $G$ or $H$. The network in Figure 2 shows the expected net profit, in tens of pounds, that he will gain on each day according to the route he chooses.
Use dynamic programming to find the route which should maximise the salesman's net profit. State the expected profit from using this route.\\
(10 marks)\\
\hfill \mbox{\textit{Edexcel D2 Q4 [10]}}