The bin packing decision problem is that given an unlimited number of bins, each of capacity 1, and n objects with sizes s1, s2, . . . , sn, where 0 < si 1, do the objects fit in k bins? 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.