4. $$\begin{array} { l l l l l l l l l l l } 25 & 9 & 32 & 16 & 17 & 23 & 18 & 12 & 4 & 8 & 40 \end{array}$$ The numbers in the list represent the weights, in kilograms, of eleven suitcases. The suitcases are to be transported in containers that will each hold a maximum weight of 50 kg .

1. Calculate a lower bound for the number of containers needed. You must make your method clear.
2. Use the first-fit bin packing algorithm to allocate the suitcases to the containers.
3. Carry out a quick sort to produce a list of the weights 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 allocate the suitcases to the containers. The two heaviest suitcases are replaced with two suitcases both of which weigh \(x \mathrm {~kg}\). It is given that the lower bound for the number of containers needed is now one less than the number found in (a).
5. Determine the range of values for \(x\). You should make your working clear.