| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2017 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Parametric objective analysis |
| Difficulty | Standard +0.8 This question requires reading constraints from a graph, finding intersection points, applying the objective function test, and most challengingly, determining the range of λ where a specific vertex remains optimal—requiring understanding of how objective function gradients relate to constraint boundaries. The parametric analysis in part (d) elevates this beyond routine linear programming. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06b Slack variables: converting inequalities to equations7.06c Working with constraints: algebra and ad hoc methods7.06e Sensitivity analysis: effect of changing coefficients |
5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{65fb7699-4301-47d2-995d-713ee33020c8-06_1517_1527_226_274}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{center}
\end{figure}
Figure 5 shows the constraints of a linear programming problem in $x$ and $y$, where $R$ is the feasible region.
\begin{enumerate}[label=(\alph*)]
\item Write down the inequalities that form region $R$.
\item Find the exact coordinates of the vertices of the feasible region.
The objective is to maximise $P$, where $P = 2 x + 3 y$
\item Use point testing to find the optimal vertex, V, of the feasible region.
The objective is changed to maximise $Q$, where $Q = 2 x + \lambda y$\\
Given that $\lambda$ is a constant and V is still the only optimal vertex of the feasible region,
\item find the range of possible values of $\lambda$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2017 Q5 [11]}}