| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2019 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Formulation from word problem |
| Difficulty | Moderate -0.5 This is a standard linear programming formulation question from D1, requiring students to define variables, write constraint inequalities from a table, and set up an objective function. While it involves multiple constraints (cutting, assembly, packaging), the process is mechanical and follows a well-practiced template with no novel problem-solving required. |
| Spec | 7.06a LP formulation: variables, constraints, objective function |
| VIIIV SIUI NI IIIUM IONOO | VIAV SIHI NI JALYM LON OO | VEYV SIHI NI JLIYM LON OO |
| VIAN SIHI NI III M I ION OC | VI4V SIHI NI ALIVM IONOO | VJYV SIHI NI JLIYM LON OO |
|
| |||
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Maximise \(50x + 150y\) Subject to: \(x + 4y \le 30\) \(3x + 8y \le 70\) \(5x + 6y \le 90\) (\(x \ge 0, y \ge 0\)) | B1 M1 A1 | (3) |
| [Graph showing feasible region with constraints] | B1 | |
| B1 | ||
| B1 | ||
| B1 | (4) | |
| Correct objective line drawn | B1 | (2) |
| V labelled correctly | B1 | |
| 10 Manhattan and 5 Brooklyn bookcases | B1 | (2) |
| Answer/Working | Marks | Guidance |
|---|---|---|
| Maximise $50x + 150y$ Subject to: $x + 4y \le 30$ $3x + 8y \le 70$ $5x + 6y \le 90$ ($x \ge 0, y \ge 0$) | B1 M1 A1 | (3) |
| [Graph showing feasible region with constraints] | B1 | |
| | B1 | |
| | B1 | |
| | B1 | (4) |
| Correct objective line drawn | B1 | (2) |
| V labelled correctly | B1 | |
| 10 Manhattan and 5 Brooklyn bookcases | B1 | (2) |7. A company makes two types of wooden bookcase, the Manhattan and the Brooklyn. The pieces of wood used for each bookcase go through three stages. They must be cut, assembled and packaged.
The table below shows the time, in hours, needed to complete each of the three stages for a single bookcase, and the profit made, in pounds, when each type of bookcase is sold. The table also shows the amount of time, in hours, that is available each week for each of the three stages.
Shortest route: $\_\_\_\_$\\
Length of shortest route: $\_\_\_\_$\\
3.
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{e7f89fa1-0afa-4aec-a430-14ec98f487c8-14_896_1514_293_200}
\end{center}
\section*{Diagram 1}
\section*{Grid 1}
4.
$\begin{array} { l l l l l l l l l l l } 180 & 80 & 250 & 115 & 100 & 230 & 150 & 95 & 105 & 90 & 390 \end{array}$
$\begin{array} { l l l l l l l l l l l } 180 & 80 & 250 & 115 & 100 & 230 & 150 & 95 & 105 & 90 & 390 \end{array}$
5.
\begin{enumerate}
\item (a)\\
\includegraphics[max width=\textwidth, alt={}, center]{e7f89fa1-0afa-4aec-a430-14ec98f487c8-22_616_1477_735_230}\\
\end{enumerate}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e7f89fa1-0afa-4aec-a430-14ec98f487c8-23_609_1468_310_239}
\captionsetup{labelformat=empty}
\caption{Figure 3\\[0pt]
[The weight of the network is $20 \mathrm { x } + 17$ ]}
\end{center}
\end{figure}
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
VIIIV SIUI NI IIIUM IONOO & VIAV SIHI NI JALYM LON OO & VEYV SIHI NI JLIYM LON OO \\
\hline
\end{tabular}
\end{center}
7.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
VIAN SIHI NI III M I ION OC & VI4V SIHI NI ALIVM IONOO & VJYV SIHI NI JLIYM LON OO \\
\hline
\end{tabular}
\end{center}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e7f89fa1-0afa-4aec-a430-14ec98f487c8-27_1734_1538_299_210}
\captionsetup{labelformat=empty}
\caption{Diagram 1}
\end{center}
\end{figure}
\begin{center}
\begin{tabular}{|l|l|}
\hline
\begin{tabular}{l}
(Total 13 marks) \\
\end{tabular} & \begin{tabular}{l}
Leave blank \\
Q7 \\
\end{tabular} \\
\hline
& \\
\hline
\end{tabular}
\end{center}
\hfill \mbox{\textit{Edexcel D1 2019 Q7 [13]}}