1 Sam is packing for a holiday. The table shows the mass of each item to be packed.
| Item | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) |
| Mass (kg) | 3 | 4 | 3.5 | 2.5 | 6 | 7.5 | 8 | 5 |
Sam's bags can each carry 10 kg , but no more.
- Use first-fit to show a possible packing that Sam could use. Indicate the items by using the letters \(A , B , \ldots\) rather than their masses.
The total mass of the 8 items is 39.5 kg . Sam says that this means they can be packed using just 4 bags.
- Explain why Sam cannot pack the items using just 4 bags.
Sam is only allowed to take 4 bags. Each item is given a value out of 20 representing how important it is to Sam.
| Item | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) |
| Mass (kg) | 3 | 4 | 3.5 | 2.5 | 6 | 7.5 | 8 | 5 |
| Value | 6 | 10 | 12 | 10 | 16 | 12 | 20 | 14 |
- Sam wishes to pack items with a large total value.
- State which item Sam should leave behind to maximise the total value.
- Write down a possible packing with this item omitted.
- Explain why no larger total is possible.