Unformatted text preview: exceed her knapsack’s capacity, and maximizes the “pleasure of the trip”, that is, the total utilities of the items. The volume and utility of each item is known to her, and she is allowed to take several copies of the same item. Formulate the problem as ﬁnding the longest path in an acyclic directed graph with the data given below; that is, write down what the nodes, arcs and arc costs represent in your model, and show why the length of a longest path (between certain nodes) gives the pleasure of an optimal packing. Then solve the problem. Is the optimal solution unique? The knapsack has capacity 6, the hiker can take apples, maps, extra sweatshirts and textbooks with her; the respective volumes of these items are in order 1 , 2 , 3 , 4; the utilities 5 , 10 , 20 and 35....
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- Fall '05
- Graph Theory, Shortest path problem