Reverse engineering objective from solution

5. \begin{figure}[h] \end{figure} Figure 3 shows the constraints of a linear programming problem in \(x\) and \(y\). The unshaded area, including its boundaries, forms the feasible region, \(R\). The four vertices of \(R\) are \(A ( 6,8 ) , B ( 13,12 ) , C ( 9,22 )\) and \(D ( 5,18 )\).
An objective line has been drawn and labelled on the graph.
When the objective function, \(P\), is maximised, the value of \(P\) is 540
When the objective function, \(P\), is minimised, the value of \(P\) is \(k\) Determine the value of \(k\). You must make your method and working clear.
(You may assume that the objective function, \(P\), takes the form \(a x + b y\) where \(a\) and \(b\) are constants.)

4. \begin{figure}[h] \end{figure} Figure 3 shows the constraints of a maximisation linear programming problem in \(x\) and \(y\), where \(x \geqslant 0\) and \(y \geqslant 0\). The unshaded area, including its boundaries, forms the feasible region, \(R\). An objective line has been drawn and labelled on the graph.

1. List the constraints as simplified inequalities with integer coefficients. The optimal value of the objective function is 216
2. 1. Calculate the exact coordinates of the optimal vertex.
   2. Hence derive the objective function. Given that \(x\) represents the number of small flower pots and \(y\) represents the number of large flower pots supplied to a customer,
3. deduce the optimal solution to the problem. TOTAL FOR DECISION MATHEMATICS 1 IS 40 MARKS END

4. \begin{figure}[h] \end{figure} Figure 3 shows the constraints of a linear programming problem in \(x\) and \(y\). The unshaded area, including its boundaries, forms the feasible region, \(R\). An objective line has been drawn and labelled on the graph.

1. State the inequalities that define the feasible region. The maximum value of the objective function is \(\frac { 160 } { 3 }\) The minimum value of the objective function is \(\frac { 883 } { 41 }\)
2. Determine the objective function, showing your working clearly.

4. \begin{figure}[h] \end{figure} Figure 3 shows the constraints of a linear programming problem in \(x\) and \(y\), where \(R\) is the feasible region. Figure 3 also shows an objective line for the problem and the optimal vertex, which is labelled as \(V\). The value of the objective at \(V\) is 556
Express the linear programming problem in algebraic form. List the constraints as simplified inequalities with integer coefficients and determine the objective. Please check the examination details below before entering your candidate information
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Candidate Number Level 3 GCE \includegraphics[max width=\textwidth, alt={}, center]{a2a6e659-aab5-4eec-9af4-ca6ab895f1c8-09_122_433_356_991}
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□ \section*{Thursday 14 May 2020} Afternoon
Paper Reference 8FMO/27 \section*{Further Mathematics} Advanced Subsidiary
Further Mathematics options
27: Decision Mathematics 1
(Part of options D, F, H and K) \section*{Answer Book} Do not return the question paper with the answer book.
1. \(\begin{array} { l l l l l l l l l l } 3.7 & 2.5 & 5.4 & 1.9 & 2.7 & 3.2 & 3.1 & 2.7 & 4.2 & 2.0 \end{array}\)

1. (a)

\begin{figure}[h] \end{figure} \begin{figure}[h] \end{figure} 3. \begin{figure}[h] \end{figure} [The weight of the network is \(5 x + 246\) ] 4. \begin{figure}[h] \end{figure}