4. $$\begin{array} { l l l l l l l l l l l } 180 & 80 & 250 & 115 & 100 & 230 & 150 & 95 & 105 & 90 & 390 \end{array}$$ The numbers in the list above represent the weights, in kilograms, of 11 boxes. John must transport all the boxes using his van. You may assume the van has sufficient space for any combination of boxes. Each van load of boxes must weigh at most 475 kg .

1. Calculate a lower bound for the number of van loads needed to transport all 11 boxes.
2. Use the first-fit bin packing algorithm to show how the boxes could be put into van loads. State the number of van loads needed according to this solution.
3. Carry out a quick sort on the numbers in the list given above 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 on your ordered list to show how the boxes could be put into van loads. State the number of van loads needed according to this solution. Due to volume restrictions, the van cannot transport more than three boxes at any one time.
5. Show how the boxes could now be put into the minimum number of van loads.