| Exam Board | AQA |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Dual objective optimization |
| Difficulty | Moderate -0.3 This is a standard D1 linear programming question requiring routine application of vertex testing for optimization and reading constraints from a diagram. While it has multiple parts, each involves straightforward procedures (evaluating objective functions at vertices, writing inequalities from boundary lines) with no novel problem-solving or conceptual challenges, making it slightly easier than average. |
| Spec | 7.06d Graphical solution: feasible region, two variables7.06e Sensitivity analysis: effect of changing coefficients |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct application of Dijkstra's algorithm, permanent labels shown | M1 A1 | M1 correct method, A1 working values |
| All permanent labels correct | A1 A1 | |
| Shortest time stated | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct route corresponding to shortest path | B1 | Follow through from (i) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Time from \(D\) to \(A\) + 3 minutes loading + shortest time \(A\) to \(J\) | M1 | |
| Correct arrival time calculated | A1 |
# Question 4:
## Part (a)(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct application of Dijkstra's algorithm, permanent labels shown | M1 A1 | M1 correct method, A1 working values |
| All permanent labels correct | A1 A1 | |
| Shortest time stated | A1 | |
## Part (a)(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct route corresponding to shortest path | B1 | Follow through from (i) |
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Time from $D$ to $A$ + 3 minutes loading + shortest time $A$ to $J$ | M1 | |
| Correct arrival time calculated | A1 | |4 The diagram shows the feasible region of a linear programming problem.\\
\includegraphics[max width=\textwidth, alt={}, center]{194d16e0-8e05-45c0-8948-99808440ed2a-005_1349_1395_408_294}
\begin{enumerate}[label=(\alph*)]
\item On the feasible region, find:
\begin{enumerate}[label=(\roman*)]
\item the maximum value of $2 x + 3 y$;
\item the maximum value of $3 x + 2 y$;
\item the minimum value of $- 2 x + y$.
\end{enumerate}\item Find the 5 inequalities that define the feasible region.
\end{enumerate}
\hfill \mbox{\textit{AQA D1 Q4}}