6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3aa30e8f-7d55-4c3b-8b2c-55c3e822c8a0-07_1296_1586_230_301}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The graph in Figure 2 is being used to solve a linear programming problem in \(x\) and \(y\). The three constraints have been drawn on the graph and the rejected regions have been shaded out. The three vertices of the feasible region \(R\) are labelled \(\mathrm { A } , \mathrm { B }\) and C .
- Determine the inequalities that define \(R\).
(2)
The objective function, \(P\), is given by
$$P = a x + b y$$
where \(a\) and \(b\) are positive constants.
The minimum value of \(P\) is 8 and the maximum value of \(P\) occurs at C . - Find the range of possible values of \(a\). You must make your method clear.
(5)