1. $$\begin{array} { l l l l l l l l l l l } 2.5 & 0.9 & 3.1 & 1.4 & 1.5 & 2.0 & 1.9 & 1.2 & 0.3 & 0.4 & 3.9 \end{array}$$ The numbers in the list are the lengths, in metres, of eleven pieces of wood. They are to be cut from planks of wood of length 5 metres. You should ignore wastage due to cutting.

1. Calculate a lower bound for the number of planks needed. You must make your method clear.
2. Use the first-fit bin packing algorithm to determine how these pieces could be cut from 5 metre planks.
3. Carry out a quick sort to produce a list of the lengths in descending order. You should show the result of each pass and identify your pivots clearly.
4. Use the first-fit decreasing bin packing algorithm to determine how these pieces could be cut from 5 metre planks.