5 The feasible region of a linear programming problem is defined by
$$\begin{aligned}
x + y & \leqslant 60
2 x + y & \leqslant 80
y & \geqslant 20
x & \geqslant 15
y & \geqslant x
\end{aligned}$$
- On the grid opposite, draw a suitable diagram to represent these inequalities and indicate the feasible region.
- In each of the following cases, use your diagram to find the maximum value of \(P\) on the feasible region. In each case, state the corresponding values of \(x\) and \(y\).
- \(P = x + 4 y\)
- \(P = 4 x + y\)