4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{89702b66-cefb-484b-9c04-dd2be4fe2250-05_1524_1360_203_356}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows the constraints of a linear programming problem in \(x\) and \(y\), where \(R\) is the feasible region. The equations of two of the lines are shown on the graph.
- Determine the inequalities that define the feasible region.
- Find the exact coordinates of the vertices of the feasible region.
The objective is to maximise \(P\), where \(P = 2 x + k y\)
- For the case \(k = 3\), use the point testing method to find the optimal vertex of the feasible region and state the corresponding value of \(P\).
- Determine the range of values for \(k\) for which the optimal vertex found in (c) is still optimal.