4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bd357978-6464-43fd-854f-4188b5408e91-06_1171_1758_269_150}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows the constraints of a linear programming problem in \(x\) and \(y\), where \(R\) is the feasible region.
- Write down the inequalities that define \(R\).
The objective is to maximise \(P\), where \(P = 3 x + y\)
- Obtain the exact value of \(P\) at each of the three vertices of \(R\) and hence find the optimal vertex, \(V\).
The objective is changed to maximise \(Q\), where \(Q = 3 x + a y\). Given that \(a\) is a constant and the optimal vertex is still \(V\),
- find the range of possible values of \(a\).