Question

The network below shows a network of railway lines from city 1 to city 10. The numbers on the arcs represent the number of cars per hour that can pass along that segment of track 400 600 300 150 500 200 400 600 450 10 6 300 300 300 200 300 500 500. 400 350 Find the maximal flow in cars per hour that can pass through the network from node 1 to node 10. In each blank, enter the following information. If there is no flow along an arc, enter 0. maximal flow (enter as 1400, blank #1 not 1,400) flow from node 1 to node 2 blank #2 blank #3 flow from node 1 to node 3 flow from node 1 to node 4 blank #4 flow from node 2 to node 5 blank #5 flow from node 2 to node 6 blank #6 flow from node 3 to node 7 flow from node 3 to node 9 blank #7 blank #8 blank #9 flow from node 4 to node 7 blank #10 flow from node 5 to node 8 flow from node 5 to node 8 blank #10 flow from node 5 to node 10 blank #11 flow from node 6 to node 5 blank #12 blank #13 flow from node 7 to node 3 blank #14 flow from node 7 to node 9 blank #15 flow from node 8 to node 5 blank #16 flow from node 8 to node 9 blank #17 flow from node 8 to node 10 blank #18 flow from node 9 to node 8 blank #19 flow from node 9 to node 10

Answer 1

Answer:---------------

Min X_F1
s.t.
X₁₂ + X₁₅ + X₁₆ - X_F1= 0

X₂₃ + X₂₄ - X₁₂= 0

X₃₄ - X₂₃= 0

X₄₈ + X_4F - X_24- - X₃₄ - X₈₄= 0

X₅₇ - X₁₅= 0

X₆₇+ X₆₉ - X₁₆ - X₇₆= 0

X₇₆+ X₇₉ - X₅₇ - X₆₇= 0

X₈₄+ X₈₉ + X_8F - X₄₈ - X₉₈= 0

X₉₈+ X_9F - X₆₉ - X₇₉ - X₈₉= 0

X_F1 -X_4F - X_8F -X_9F= 0

X₁₂  ≥  500

X₁₅ ≥ 300

X₁₆ ≥ 600

X₂₃ ≥ 300

X₂₄ ≥ 400

X₃₄ ≥ 150

X₄₈ ≥ 400

X_4F ≥ 600

X₅₇ ≥ 400

X₆₇ ≥ 300

X₆₉ ≥ 500

X₇₆ ≥ 200

X₇₉ ≥ 350

X₈₄ ≥ 200

X₈₉ ≥ 300

X_8F ≥ 450

X₉₈ ≥ 300

X_9F ≥ 500

X_ij ≥ 0 for all i,j