5 The constraints of a linear programming problem are represented by the graph below. The feasible region is the unshaded region, including its boundaries.
\includegraphics[max width=\textwidth, alt={}, center]{197624b2-ca67-4bad-9c2c-dc68c10be0fd-04_1118_816_404_662}

1. Write down four inequalities that define the feasible region. The objective is to maximise \(P = 5 x + 3 y\).
2. Using the graph or otherwise, obtain the coordinates of the vertices of the feasible region and hence find the values of \(x\) and \(y\) that maximise \(P\), and the corresponding maximum value of \(P\). The objective is changed to maximise \(Q = a x + 3 y\).
3. For what set of values of \(a\) is the maximum value of \(Q\) equal to 3?