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 ±ow problem: (I am using the notation from class b i < 0 is a supply. The ²rst 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, ²nd 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
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This note was uploaded on 01/31/2011 for the course AMS 540 taught by Professor Arkin,e during the Fall '08 term at SUNY Stony Brook.

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

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