6 William is making the bridesmaid dresses and pageboy outfits for his sister's wedding. He expects it to take 20 hours to make each bridesmaid dress and 15 hours to make each pageboy outfit. Each bridesmaid dress uses 8 metres of fabric. Each pageboy outfit uses 3 metres of fabric. The fabric costs \(\pounds 8\) per metre. Additional items cost \(\pounds 35\) for each bridesmaid dress and \(\pounds 80\) for each pageboy outfit. William's sister wants to have at least one bridesmaid and at least one pageboy. William has 100 hours available and must not spend more than \(\pounds 600\) in total on materials. Let \(x\) denote the number of bridesmaids and \(y\) denote the number of pageboys.

1. Show why the constraint \(4 x + 3 y \leqslant 20\) is needed and write down three more constraints on the values of \(x\) and \(y\), other than that they must be integers.
2. Plot the feasible region where all four constraints are satisfied. William's sister wants to maximise the total number of attendants (bridesmaids and pageboys) at her wedding.
3. Use your graph to find the maximum number of attendants.
4. William costs his time at \(\pounds 15\) an hour. Find, and simplify, an expression, in terms of \(x\) and \(y\), for the total cost (for all materials and William’s time). Hence find, and interpret, the minimum cost solution to part (iii).