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Unformatted text preview: 4 2 6 [3] 8 [4] [2] (a) Write the primal and dual linear programs for the MCF problem. (b) Based on complementary slackness conditions, verify the optimality of each of the following primal solutions: i. x 12 = 3 ,x 23 = 4 ,x 24 = 4 ,x 45 = 2 ii. x 13 = 3 ,x 24 = 5 ,x 43 = 1 ,x 45 = 2 iii. x 13 = 2 ,x 12 = 1 ,x 43 = 2 ,x 24 = 6 ,x 45 = 2 4. Consider the uncapacitated MCF problem where the number along each arc represents the unit cost and the value beside the vertices denote the supply/demand. 1 2 4 3 2 4 4 1 2 [2] [5] [3] (a) Start with the spanning tree solution consisting of arcs T = { (1 , 2) , (2 , 4) , (1 , 3) } and use the network simplex method to solve the problem to optimality. (b) By how much can we increase the cost of arc (2 , 3) and still have the same optimal basic feasible solution? 2...
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This note was uploaded on 12/02/2011 for the course MATH 3252 taught by Professor Tanbanpin during the Spring '10 term at National University of Singapore.
 Spring '10
 TanBanPin
 Math

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