8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{818ba207-5839-4698-aacb-75dab88b218f-10_1753_1362_260_315}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
The graph in Figure 4 is being used to solve a linear programming problem. The four constraints have been drawn on the graph and the rejected regions have been shaded out. The four vertices of the feasible region \(R\) are labelled \(\mathrm { A } , \mathrm { B } , \mathrm { C }\) and D .
- Write down the constraints represented on the graph.
(2)
The objective function, P , is given by
$$\mathrm { P } = x + k y$$
where \(k\) is a positive constant.
The minimum value of the function P is given by the coordinates of vertex A and the maximum value of the function P is given by the coordinates of vertex D . - Find the range of possible values for \(k\). You must make your method clear.
(Total 8 marks)