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Unformatted text preview: ENGRI 115 Engineering Applications of OR Fall 2007 Solutions Prelim 2 1. (50 points) Given the following transportation problem with supply centers i = 1 , 2 , 3 and demand centers j = 1 , 2 , 3: j 1 2 3 d j 5 10 9 i s i c ij 1 6 3 4 9 2 7 10 10 20 3 11 13 9 18 An initial solution is given by x 11 = 5 , x 13 = 1 , x 22 = 7 , x 32 = 3 , x 33 = 8, and all other x ij s set to 0. Consider the algorithm taught in class to solve transportation problems starting with this initial solution. (a) (25) In the first step we would look for an edge for which increase in shipment would be profitable. Carry out this step only for edge ( i, j ) = (2 , 1), i.e., determine the net unit cost change for this edge. Show all your work. (b) (20) In the previous step we determined that it is profitable to increase shipment along edge (2 , 1). Thus the algorithm could select this edge and adjust the ship- ment. What is the resulting new solution? Give all the x ij s graphically or in a list. (c) (5) What is the total shipment cost of the new solution? Answer: The answer to (a), (b) and (c) is given on the next page. 2. (50 points) Below you find a list of statements. Determine for each statement whether2....
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- Fall '05