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]{ccb12789-cd5f-40dc-9f10-f8bb45399580-4_919_917_322_575}

1. Obtain the four inequalities that define the feasible region.
2. Calculate the coordinates of the vertices of the feasible region, giving your values as fractions. The objective is to maximise \(P = x + 4 y\).
3. Calculate the value of \(P\) at each vertex of the feasible region. Hence write down the coordinates of the optimal point, and the corresponding value of \(P\). Suppose that the solution must have integer values for both \(x\) and \(y\).
4. Find the coordinates of the optimal point with integer-valued \(x\) and \(y\), and the corresponding value of \(P\). Explain how you know that this is the optimal solution.