Example 2 xAB:amount of flow of the short route xA:amount of flow of the long route Variables: 0 XAB,XAB XBC,XBC,XAC,XAC- Constraints: A 口XAB+XAB+xAC+XAC≤12 (edge (A,a)) 12 口XAB+XAB+XBC+xBC≤10 (edge(B,b)) 口 XBC+XBC+XAC+XAC≤8 (edge (C,c)) 6 11 0 XAB+XBC+xAC≤6 (edge (a,b)) 0 XAC+xAB+XBC≤13 (edge (b,c)) b 13 xAB+xBc+x4c≤11 (edge (a,c)) 10 XAB,XAB,XBC,XBC,XAC,XAC>0 B 同 Objective: max 3(xAB +xAB)+2(xBC +xBc)+4(xAC +xAc) 7Example 2 ◼ Variables: ❑ 𝑥𝐴𝐵, 𝑥𝐴𝐵 ′ ,𝑥𝐵𝐶,𝑥𝐵𝐶 ′ ,𝑥𝐴𝐶,𝑥𝐴𝐶 ′ . ◼ Constraints: ❑ 𝑥𝐴𝐵 + 𝑥𝐴𝐵 ′ + 𝑥𝐴𝐶 + 𝑥𝐴𝐶 ′ ≤ 12 (edge (𝐴, 𝑎)) ❑ 𝑥𝐴𝐵 + 𝑥𝐴𝐵 ′ + 𝑥𝐵𝐶 + 𝑥𝐵𝐶 ′ ≤ 10 (edge (𝐵, 𝑏)) ❑ 𝑥𝐵𝐶 + 𝑥𝐵𝐶 ′ + 𝑥𝐴𝐶 + 𝑥𝐴𝐶 ′ ≤ 8 (edge (𝐶, 𝑐)) ❑ 𝑥𝐴𝐵 + 𝑥𝐵𝐶 ′ + 𝑥𝐴𝐶 ′ ≤ 6 (edge (𝑎, 𝑏)) ❑ 𝑥𝐴𝐶 ′ + 𝑥𝐴𝐵 ′ + 𝑥𝐵𝐶 ≤ 13 (edge (𝑏, 𝑐)) ❑ 𝑥𝐴𝐵 + 𝑥𝐵𝐶 ′ + 𝑥𝐴𝐶 ′ ≤ 11 (edge (𝑎, 𝑐)) ❑ 𝑥𝐴𝐵, 𝑥𝐴𝐵 ′ ,𝑥𝐵𝐶,𝑥𝐵𝐶 ′ ,𝑥𝐴𝐶,𝑥𝐴𝐶 ′ ≥ 0 ◼ Objective: max 3(𝑥𝐴𝐵 + 𝑥𝐴𝐵 ′ ) + 2(𝑥𝐵𝐶 + 𝑥𝐵𝐶 ′ ) + 4(𝑥𝐴𝐶 + 𝑥𝐴𝐶 ′ ) 𝑥𝐴𝐵: amount of flow of the short route 𝑥𝐴𝐵 ′ : amount of flow of the long route 7