2 [Figure 1, printed on the insert, is provided for use in this question.]
The feasible region of a linear programming problem is represented by $$\begin{aligned} x + y & \leqslant 30
2 x + y & \leqslant 40
y & \geqslant 5
x & \geqslant 4
y & \geqslant \frac { 1 } { 2 } x \end{aligned}$$

1. On Figure 1, draw a suitable diagram to represent these inequalities and indicate the feasible region.
2. Use your diagram to find the maximum value of \(F\), on the feasible region, in the case where:
   1. \(F = 3 x + y\);
   2. \(F = x + 3 y\).