5 The feasible region of a linear programming problem is determined by the following:
$$\begin{aligned}
x & \geqslant 1
y & \geqslant 3
x + y & \geqslant 5
x + y & \leqslant 12
3 x + 8 y & \leqslant 64
\end{aligned}$$
- On the grid below, draw a suitable diagram to represent the inequalities and indicate the feasible region.
- Use your diagram to find, on the feasible region:
- the maximum value of \(3 x + y\);
- the maximum value of \(2 x + 3 y\);
- the minimum value of \(- 2 x + y\).
In each case, state the coordinates of the point corresponding to your answer.
[0pt]
[6 marks]