1 Five boxes weigh \(5 \mathrm {~kg} , 2 \mathrm {~kg} , 4 \mathrm {~kg} , 3 \mathrm {~kg}\) and 8 kg . They are stacked, in the order given, with the first box at the top of the stack. The boxes are to be packed into bins that can each hold up to 10 kg .

1. Use the first-fit method to put the boxes into bins. Show clearly which boxes are packed in which bins.
2. Use the first-fit decreasing method to put the boxes into bins. You do not need to use an algorithm for sorting. Show clearly which boxes are packed in which bins.
3. Why might the first-fit decreasing method not be practical?
4. Show that if the bins can only hold up to 8 kg each it is still possible to pack the boxes into three bins.