CO-351-1075-Midterm_exam

CO-351-1075-Midterm_exam - ID Page 2 of 8 a-2-2 c d 1 s-2-1...

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ID: Page 2 of 8 -2 1 2 -2 -1 4 -2 1 -1 1 c a b s d e f Problem 1: [10 marks] Using Dantzig’s 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.)
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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 i -th 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 i -days 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.
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ID: Page 4 of 8 Problem 3: [10 marks] Let D = ( N, A ) be a digraph with arc-lengths ( w uv : uv A ), and let s, t N . Now let b s = - 1, b t = 1, and b v
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