4.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{ca57c64b-0b33-4179-be7f-684bd6ea2162-07_1105_1249_312_512}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}

Figure 4 shows three of the six constraints for a linear programming problem in $x$ and $y$ The unshaded region and its boundaries satisfy these three constraints.
\begin{enumerate}[label=(\alph*)]
\item State these three constraints as simplified inequalities with integer coefficients.

The variables $x$ and $y$ represent the number of orange fish and the number of blue fish, respectively, that are to be kept in an aquarium.

The number of fish in the aquarium is subject to these three further constraints

\begin{itemize}
  \item there must be at least one blue fish
  \item the orange fish must not outnumber the blue fish by more than ten
  \item there must be no more than five blue fish for every orange fish
\item Write each of these three constraints as a simplified inequality with integer coefficients.
\item Represent these three constraints by adding lines and shading to Diagram 1 in the answer book, labelling the feasible region, $R$
\end{itemize}

The total value (in pounds) of the fish in the aquarium is given by the objective function

$$\text { Maximise } P = 3 x + 5 y$$
\item \begin{enumerate}[label=(\roman*)]
\item Use the objective line method to determine the optimal point of the feasible region, giving its coordinates as exact fractions.
\item Hence find the maximum total value of the fish in the aquarium, stating the optimal number of orange fish and the optimal number of blue fish.

\begin{table}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Please check the examination details below before entering your candidate information}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
\multicolumn{8}{|c|}{Candidate surname} & Other names \\
\hline
\multicolumn{4}{|l|}{Centre Number} & \multicolumn{4}{|l|}{Candidate Number} &  \\
\hline
□ &  &  & □ &  &  &  &  &  \\
\hline
\end{tabular}
\end{center}
\end{table}

\section*{Pearson Edexcel Level 3 GCE}
\section*{Friday 17 May 2024}
Afternoon

\section*{Further Mathematics}
Advanced Subsidiary\\
Further Mathematics options\\
27: Decision Mathematics 1\\
(Part of options D, F, H and K)

\section*{D1 Answer Book}
Do not return the question paper with the answer book.\\
1.\\
$\begin{array} { l l l l l l l l l l l } 4 & 6.5 & 7 & 1.3 & 2 & 5 & 1.5 & 6 & 4.5 & 6 & 1 \end{array}$

2.

\begin{center}
\includegraphics[max width=\textwidth, alt={}]{ca57c64b-0b33-4179-be7f-684bd6ea2162-12_435_815_392_463}
\end{center}

\section*{Diagram 1}
Use this diagram only if you need to redraw your activity network.\\
\includegraphics[max width=\textwidth, alt={}, center]{ca57c64b-0b33-4179-be7f-684bd6ea2162-12_442_820_2043_458}

Copy of Diagram 1

\begin{center}
\begin{tabular}{|l|l|l|}
\hline
VJYV SIHI NI JIIYM ION OC & V346 SIHI NI JLIYM ION OC & V34V SIHI NI IIIIM ION OC \\
\hline

\hline
\end{tabular}
\end{center}

Key:

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{ca57c64b-0b33-4179-be7f-684bd6ea2162-13_1217_1783_451_236}
\captionsetup{labelformat=empty}
\caption{Diagram 2}
\end{center}
\end{figure}

3.\\
\includegraphics[max width=\textwidth, alt={}, center]{ca57c64b-0b33-4179-be7f-684bd6ea2162-14_2463_1240_339_465}\\
Shortest route from A to M:\\
Length of shortest route from A to M:\\

\begin{center}
\includegraphics[max width=\textwidth, alt={}]{ca57c64b-0b33-4179-be7f-684bd6ea2162-16_3038_2264_0_0}
\end{center}

\begin{center}
\includegraphics[max width=\textwidth, alt={}]{ca57c64b-0b33-4179-be7f-684bd6ea2162-17_1103_1247_397_512}
\end{center}

\section*{Diagram 1}
\section*{There is a copy of Diagram 1 on page 11 if you need to redraw your graph.}

\begin{center}
\begin{tabular}{|l|l|l|}
\hline
VJYV SIHI NI JIIIM ION OC & V341 S1H1 NI JLIYM ION OA & V34V SIHI NI IIIVM ION OC \\
\hline

\hline
\end{tabular}
\end{center}

Use this diagram only if you need to redraw your graph.\\
\includegraphics[max width=\textwidth, alt={}, center]{ca57c64b-0b33-4179-be7f-684bd6ea2162-19_1108_1252_1606_509}

Copy of Diagram 1
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{Edexcel FD1 AS 2024 Q4 [12]}}