| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2023 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Parametric objective analysis |
| Difficulty | Standard +0.3 This is a standard D1 linear programming question with routine parts (a)-(c) involving reading constraints, finding vertices, and point testing. Part (d) requires understanding when the objective gradient changes optimality, which is a common exam technique but slightly elevates difficulty above average. |
| Spec | 7.06d Graphical solution: feasible region, two variables7.06e Sensitivity analysis: effect of changing coefficients |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | 0.4 | 0 |
I appreciate your request, but I'm unable to complete this task as written. The content you've provided appears to be incomplete or improperly formatted:
```
Question 4:
4 | 0.4 | 0 | 0 | 4
```
This doesn't contain:
- Marking annotations (M1, A1, B1, DM1, etc.)
- Guidance notes
- Mathematical content with Unicode symbols to convert to LaTeX
- Clear marking criteria
Could you please provide:
1. The complete extracted mark scheme for Question 4, or
2. A larger sample of the mark scheme content you'd like cleaned up?4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{89702b66-cefb-484b-9c04-dd2be4fe2250-05_1524_1360_203_356}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
Figure 2 shows the constraints of a linear programming problem in $x$ and $y$, where $R$ is the feasible region. The equations of two of the lines are shown on the graph.
\begin{enumerate}[label=(\alph*)]
\item Determine the inequalities that define the feasible region.
\item Find the exact coordinates of the vertices of the feasible region.
The objective is to maximise $P$, where $P = 2 x + k y$
\item For the case $k = 3$, use the point testing method to find the optimal vertex of the feasible region and state the corresponding value of $P$.
\item Determine the range of values for $k$ for which the optimal vertex found in (c) is still optimal.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2023 Q4 [11]}}