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Unformatted text preview: ID: Page 2 of 82 1 221 42 11 1 c a b s d e f Problem 1: [10 marks] Using Dantzigs Algorithm, either find a tree of shortest dipaths rooted at s , or find a negative dicycle in the digraph above. (Start with the spanning tree indicated by the edges in bold.) ID: Page 3 of 8 Problem 2: [10 marks] A company sends its products via courier to its clients. For the next n days, the number of orders on the ith day is d i . The cost of shipping d parcels in a day is p ( d ). Naturally p ( d + d ) p ( d ) + p ( d ). Thus it may be more ecconomical to delay sending out orders on one or more days to take advantage of the bulk postage rates. However, the company pays a penalty of c ( i ) for each parcel that is idays late. On which of the next n days should the company ship its parcels in order to minimize its costs (mailing plus penalties)? Formulate this problem as a shortest ( s, t )dipath problem. ID: Page 4 of 8 Problem 3: [10 marks] Let D = ( N, A ) be a digraph with arclengths (...
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 Fall '05
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