| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2011 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Graphical optimization with objective line |
| Difficulty | Moderate -0.5 This is a standard D1 linear programming question requiring reading constraints from a graph, plotting additional constraints, identifying the feasible region, and using an objective line to find the optimal vertex. While it involves multiple steps (6 marks total), each step follows routine procedures taught in Decision Maths with no novel problem-solving required—slightly easier than average A-level maths due to the mechanical nature of graphical LP methods. |
| Spec | 7.06d Graphical solution: feasible region, two variables |
6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{0360f78d-e18c-4c47-a2ec-ddd705a4175f-7_1214_1581_251_242}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{center}
\end{figure}
The graph in Figure 6 is being used to solve a linear programming problem. Two of the constraints have been drawn on the graph and the rejected regions shaded out.
\begin{enumerate}[label=(\alph*)]
\item Write down the constraints shown on the graph.
Two further constraints are
$$\begin{aligned}
x + y & \geqslant 30 \\
\text { and } \quad 5 x + 8 y & \leqslant 400
\end{aligned}$$
\item Add two lines and shading to Graph 1 in your answer book to represent these constraints. Hence determine the feasible region and label it R .
The objective is to
$$\text { minimise } 15 x + 10 y$$
\item Draw a profit line on Graph 1 and use it to find the optimal solution. You must label your profit line clearly.\\
(3)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2011 Q6 [11]}}