Here is a problem iI am trying to solve:
The bin packing decision problem is thatdefined as follows: given an unlimited number of bins, each of capacity 1equal to $1$, and n$n$ objects with sizes s1, s2$s_1$, .$s_2$, .$\dots$, .$s_n$ , sn, where 0 < si ≤ 1($0 < s_i ≤ 1$), do the objects fit in k$k$ bins? where k (where $k$ is a given integer.)? The bin packing optimization problem is to find the smallest number of bins into which the objects can be packed. Show that if the decision problem can be solved in polynomial time, then the optimization problem can also be solved in polynomial time.
I know what it is asking but iI don't know what the "optimization" problem for this is?. Is it the grouping of all the objects into different bins? e.g. s1 (for instance, s3$s_1$, $s_3$, and s6$s_6$ are in bin 1#$1$, s2$s_2$, s4$s_4$, s5$s_5$ are in bin 2#$2$, etc.)? Or is it simply the number of bins you need to store them? I feel like the number of bins is the decision problem...
