5. A linear programming problem in \(x\) and \(y\) is described as follows. Maximise \(\quad P = 2 x + 3 y\)
subject to $$\begin{aligned} x & \geqslant 25
y & \geqslant 25
7 x + 8 y & \leqslant 840
4 y & \leqslant 5 x
5 y & \geqslant 3 x
x , y & \geqslant 0 \end{aligned}$$

1. Add lines and shading to Diagram 1 in the answer book to represent these constraints. Hence determine the feasible region and label it R .
2. Use the objective line method to find the optimal vertex, V, of the feasible region. You must clearly draw and label your objective line and the vertex V.
3. Calculate the exact coordinates of vertex V. Given that an integer solution is required,
4. determine the optimal solution with integer coordinates. You must make your method clear.