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# hw9 - AMS 540 MBA 540(Fall 2010 Estie Arkin Linear...

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AMS 540 / MBA 540 (Fall, 2010) Estie Arkin Linear Programming Homework Set # 9 Due in class on Tuesday, December 7, 2010. 1). Consider the following upper bounded minimum cost netwrok flow problem: (I am using the notation from class b i < 0 is a supply. The first number next to each edge is the upper bound u ij , and the second number is the cost c ij .) 1 1 5,2 4 -2 8,-3 5 -5 1,3 2 5 2,1 1,3 6,2 4,6 4,0 3 1 (a). Use the arcs (4,1) (4,3) (3,2) (5,4) as your starting tree solution. The edge (1,2) is non basic at its upper bound, and all other non basic edges are at the lower bound of zero. Compute the x ij and the fair prices (dual variables) w i . (b). Starting from the feasible tree soltuion of part (a), using the network simplex method, find the optimal solution. 2). Construct an example of a transshipment problem with all arc costs positive and the following counterintuitive property: If the supply at a suitable source and the demand at a suitable sink are both increased by 1 unit, then the optimal cost decreases! (This can be done with an example of 4 nodes.) 3). (a). Consider the Balanced Transportation Problem min

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hw9 - AMS 540 MBA 540(Fall 2010 Estie Arkin Linear...

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