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4.22. The tramp steamer problem. You are the owner of a steamship that can ply between a group of port cities V. You make money at each port: a visit to city i earns you a profit of p, dollars. Meanwh
4.22. The tramp steamer problem. You are the owner of a steamship that can ply between a group of port cities V. You make money at each port: a visit to city i earns you a profit of p, dollars. Meanwhile, the transportation cost from port i to port j is cij > 0. You want to find a cyclic route in which the ratio of profit to cost is maximized To this end, consider a directed graph G (V, E) whose nodes are ports, and which has edges between each pair of ports. For any cycle C in this graph, the profit-to-cost ratio is 130 Let r* be the maximum ratio achievable by a simple cycle. One way to determine r is by binary search: by first guessing some ratio r, and then testing whether it is too large or too small. Consider any positive r >0. Give each edge (i,j) a weight of wiyy (a) Show that if there is a cycle of negative weight, then r
