5 The feasible region of a linear programming problem is determined by the following:
$$\begin{aligned}
y & \geqslant 20
x + y & \geqslant 25
5 x + 2 y & \leqslant 100
y & \leqslant 4 x
y & \geqslant 2 x
\end{aligned}$$
- On Figure 1 opposite, draw a suitable diagram to represent the inequalities and indicate the feasible region.
- Use your diagram to find the minimum value of \(P\), on the feasible region, in the case where:
- \(P = x + 2 y\);
- \(P = - x + y\).
In each case, state the corresponding values of \(x\) and \(y\).