| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Graphical optimization with objective line |
| Difficulty | Moderate -0.8 This is a standard D1 linear programming question requiring routine graphical methods: plotting two additional constraint lines, identifying the feasible region, writing a profit function, and using the objective line method to find optimal vertices. All techniques are textbook procedures with no novel problem-solving required, making it easier than average but not trivial due to the multi-step nature and careful graphical work needed. |
| Spec | 7.06d Graphical solution: feasible region, two variables7.06e Sensitivity analysis: effect of changing coefficients |
I notice the content provided appears to be incomplete or unclear:
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Question 8:
8
7
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There doesn't appear to be any actual mark scheme content to clean up—no marking annotations (M1, A1, B1, etc), unicode symbols to convert, or guidance notes are present.
Could you please provide the full mark scheme content for Question 8?8.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{552f3296-ad61-448b-8168-6709fb359fa2-8_1051_1385_194_365}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{center}
\end{figure}
A company produces two products, X and Y .\\
Let $x$ and $y$ be the hourly production, in kgs, of X and Y respectively.\\
In addition to $x \geqslant 0$ and $y \geqslant 0$, two of the constraints governing the production are
$$\begin{gathered}
12 x + 7 y \geqslant 840 \\
4 x + 9 y \geqslant 720
\end{gathered}$$
These constraints are shown on the graph in Figure 6, where the rejected regions are shaded out. Two further constraints are
$$\begin{gathered}
x \geqslant 20 \\
3 x + 2 y \leqslant 360
\end{gathered}$$
\begin{enumerate}[label=(\alph*)]
\item Add two lines and shading to Figure 6 in your answer book to represent these inequalities.
\item Hence determine and label the feasible region, R.
The company makes a profit of 70 p and 20 p per kilogram of X and Y respectively.
\item Write down an expression, in terms of $x$ and $y$, for the hourly profit, £P.
\item Mark points A and B on your graph where A and B represent the maximum and minimum values of P respectively. Make your method clear.\\
(4)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 Q8 [10]}}