| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Parametric objective analysis |
| Difficulty | Standard +0.8 This question requires students to extract constraints from a graph (routine D1 skill) but then analyze how a parametric objective function behaves across different vertices. Part (b) demands understanding that the optimal vertex changes as the gradient of the objective line changes, requiring comparison of slopes between adjacent edges of the feasible region—a conceptually sophisticated task that goes beyond standard textbook exercises. |
| Spec | 7.06d Graphical solution: feasible region, two variables7.06e Sensitivity analysis: effect of changing coefficients |
8.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{818ba207-5839-4698-aacb-75dab88b218f-10_1753_1362_260_315}
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\caption{Figure 4}
\end{center}
\end{figure}
The graph in Figure 4 is being used to solve a linear programming problem. The four constraints have been drawn on the graph and the rejected regions have been shaded out. The four vertices of the feasible region $R$ are labelled $\mathrm { A } , \mathrm { B } , \mathrm { C }$ and D .
\begin{enumerate}[label=(\alph*)]
\item Write down the constraints represented on the graph.\\
(2)
The objective function, P , is given by
$$\mathrm { P } = x + k y$$
where $k$ is a positive constant.
The minimum value of the function P is given by the coordinates of vertex A and the maximum value of the function P is given by the coordinates of vertex D .
\item Find the range of possible values for $k$. You must make your method clear.\\
(Total 8 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2014 Q8 [8]}}