4. \begin{figure}[h] \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.

1. 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
   • there must be at least one blue fish
   • the orange fish must not outnumber the blue fish by more than ten
   • there must be no more than five blue fish for every orange fish
   • Write each of these three constraints as a simplified inequality with integer coefficients.
   • Represent these three constraints by adding lines and shading to Diagram 1 in the answer book, labelling the feasible region, \(R\)
   The total value (in pounds) of the fish in the aquarium is given by the objective function $$\text { Maximise } P = 3 x + 5 y$$
2. 1. Use the objective line method to determine the optimal point of the feasible region, giving its coordinates as exact fractions.
   2. 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]
      \captionsetup{labelformat=empty} \caption{Please check the examination details below before entering your candidate information}

      Candidate surname								Other names
      Centre Number				Candidate Number
      □			□

      \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.
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      \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

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      Key: \begin{figure}[h]
      \includegraphics[alt={},max width=\textwidth]{ca57c64b-0b33-4179-be7f-684bd6ea2162-13_1217_1783_451_236} \captionsetup{labelformat=empty} \caption{Diagram 2}
      \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:
      
      \includegraphics[max width=\textwidth, alt={}]{ca57c64b-0b33-4179-be7f-684bd6ea2162-16_3038_2264_0_0}
      \includegraphics[max width=\textwidth, alt={}]{ca57c64b-0b33-4179-be7f-684bd6ea2162-17_1103_1247_397_512}
      \section*{Diagram 1} \section*{There is a copy of Diagram 1 on page 11 if you need to redraw your graph.}

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      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