6 An animal sanctuary has a rainwater collection site.
The manager of the sanctuary is installing a pipe system to connect the rainwater collection site to five other sites in the sanctuary.
Each site does not need to be connected directly to the rainwater collection site.
There are nine possible routes between the sites that are suitable for water pipes.
The distances, in metres, of the nine possible routes are given in the table below.
| From/To | Henhouse (H) | Goatshed (G) | Kennels (K) | Cattery (C) |
| Rainwater collection site (R) | 840 | 810 | 520 | 370 |
| Cattery (C) | - | 680 | 610 | \multirow{3}{*}{} |
| Duckpond (D) | 480 | 310 | | |
| Goatshed (G) | 150 | | | |
Water pipe costs 60 pence per metre.
Find the minimum cost of connecting all the sites to the rainwater collection site.
Fully justify your answer.
\(7 \quad\) A linear programming problem has the constraints
$$\begin{aligned}
1 \leq x & \leq 6
1 \leq y & \leq 6
y & \geq x
x + y & \leq 11
\end{aligned}$$