2 Seven items need to be packed into bins. Each bin has capacity 30 kg . The sizes of the items, in kg, in the order that they are received, are as follows.
12
23
15
18
8
7
5

1. Find the packing that results using each of these algorithms.
   1. The next-fit method
   2. The first-fit method
   3. The first-fit decreasing method
2. A student claims that all three methods from part (a) can be used for both 'online' and 'offline' lists. Explain why the student is wrong. The bins of capacity 30 kg are replaced with bins of capacity \(M \mathrm {~kg}\), where \(M\) is an integer.
   The item of size 23 kg can be split into two items, of sizes \(x \mathrm {~kg}\) and \(( 23 - x ) \mathrm { kg }\), where \(x\) may be any integer value you choose from 1 to 11. No other item can be split.
3. Determine the smallest value of \(M\) for which four bins are needed to pack these eight items. Explain your reasoning carefully.