6 [Figure 1, printed on the insert, is provided for use in this question.]
Dino is to have a rectangular swimming pool at his villa.
He wants its width to be at least 2 metres and its length to be at least 5 metres.
He wants its length to be at least twice its width.
He wants its length to be no more than three times its width.
Each metre of the width of the pool costs \(\pounds 1000\) and each metre of the length of the pool costs \(\pounds 500\). He has \(\pounds 9000\) available. Let the width of the pool be \(x\) metres and the length of the pool be \(y\) metres.

1. Show that one of the constraints leads to the inequality $$2 x + y \leqslant 18$$
2. Find four further inequalities.
3. On Figure 1, draw a suitable diagram to show the feasible region.
4. Use your diagram to find the maximum width of the pool. State the corresponding length of the pool.