4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e0c89aba-9d2e-469b-8635-d513df0b65a4-05_1198_908_226_584}
\captionsetup{labelformat=empty}
\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.
- Determine the inequalities that define the feasible region.
- Find the exact coordinates of the vertices of the feasible region.
The objective is to maximise \(P = 2 x + 3 y\).
- Use point testing at each vertex to find the optimal vertex, \(V\), of the feasible region and state the corresponding value of \(P\) at \(V\).
(3)
The objective is changed to maximise \(Q = 2 x + k y\), where \(k\) is a constant. - Find the range of values of \(k\) for which the vertex identified in (c) is still optimal.
(2)