Show that the bottleneck assignment problem defined in Example 7.4.11 is a special case of the
algebraic assignment problem; see [Law76, §5.7] and [GaTa88] for that problem. Is every optimal matching also product-optimal? Describe the problem of finding an optimal integral circulation on a network (G, b, c) as an ILP. Also, describe the problem of finding a maximal spanning tree for a network (G,w) as a ZOLP. Is this an interesting approach to the problem?