5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{65fb7699-4301-47d2-995d-713ee33020c8-06_1517_1527_226_274}
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\caption{Figure 5}
\end{figure}
Figure 5 shows the constraints of a linear programming problem in \(x\) and \(y\), where \(R\) is the feasible region.
- Write down the inequalities that form region \(R\).
- Find the exact coordinates of the vertices of the feasible region.
The objective is to maximise \(P\), where \(P = 2 x + 3 y\)
- Use point testing to find the optimal vertex, V, of the feasible region.
The objective is changed to maximise \(Q\), where \(Q = 2 x + \lambda y\)
Given that \(\lambda\) is a constant and V is still the only optimal vertex of the feasible region, - find the range of possible values of \(\lambda\).