4 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]{f2b85dfb-49df-4ea5-b118-9b95f0b27bad-03_1025_826_374_657}

1. Write down inequalities that define the feasible region.
2. Find the coordinates of the four vertices of the feasible region. The objective is to maximise \(P\), where \(P = x + 2 y\).
3. Find the values of \(x\) and \(y\) that maximise \(P\), and the corresponding maximum value of \(P\). The objective is changed to minimise \(Q\), where \(Q = 2 x - y\).
4. Find the minimum value of \(Q\) and describe the set of feasible points for which \(Q\) takes this value.
5. Show that there are no points in the feasible region for which the value of \(P\) is the same as the value of \(Q\).