3 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]{fe06fa02-9f5d-4082-8e96-feea705d3fa2-3_933_935_397_605}

1. Write down the inequalities that define the feasible region.
2. Write down the coordinates of the three vertices of the feasible region. The objective is to maximise \(2 x + 3 y\).
3. Find the values of \(x\) and \(y\) at the optimal point, and the corresponding maximum value of \(2 x + 3 y\). The objective is changed to maximise \(2 x + k y\), where \(k\) is positive.
4. Find the range of values of \(k\) for which the optimal point is the same as in part (iii).