Solutions 263
Bn
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cl 2 = [5 4600000400000 0]
2/2 = [7 4 6|0 0 0 0 0-2 0 0 0 0 0 0]
Then, the lengths of arcs are Cka + u> 0 = 1+0 = 1, V arcs except arc h, whose
length is 1 - 2 = -1.
For commodity one, the minimum shortest path P2 : a^b^d^m^-p
has length 5, which is strictly less than the corresponding dual variable wi = 7.
Thus, fi enters to the basis with the updated column
{B^lA^2 )T =[101000-1-1-100000-1]
and the updated RHS is
XB 2 = (B 2 lb)T = [fl h /l3 Sb Sd Se Sf Sg /12 Sj Si Sm Sn S 0 Sp]
xTB2 = (B^bf = [10 10 10 0 0 0 0 0 0 0 10 0 0 0 0] ;
therefore, either /x or fa leaves. We choose /1!