Example 2 xar: amount of flow of the short route xAp: amount of flow of the long route ariables 0 AB, XAB XBC, xBC, XAC, xAC Constraints 口xAB+xAB+xAC+xAC≤12(edge(A,a) 口xAB+xAB+xBC+xBC≤10(edge(B,b) 口xBC+xBC+xAC+xAC≤8(edge(C,c) 口xAB+xBC+xAc≤6 (edge(a, b)) axAc+xAB+xBC≤13 (edge(b, c)) 口xAB+xBC+xAC≤11 (edge(a, c)) 口xAB,xAB,xBC,xBC,xAC,xAC≥0 Objective: max 3 (AB+XAB)+ 2(xBC +xBC)+4(xAC Xac)Example 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