A network of railway lines connects the main lines entering and leaving a city. Speed limits, track reconstruction, and train length restrictions lead to the flow diagram below, where the numbers represent how many cars can pass per hour. Formulate an LP to find the maximal flow in cars per hour from node 1 to node F.
What will be an ideal response?
Min XF1
s.t.
X12 + X15 + X16 ? XF1 = 0
X23 + X24 ? X 12 = 0
X34 ? X23 = 0
X48 + X4F ? X24 ? X34 ? X84 = 0
X57 ? X15 = 0
X67 + X69 ? X16 ? X76 = 0
X76 + X79 ? X57 ? X67 = 0
X84 + X89 + X8F ? X48 ? X98 = 0
X98 + X9F ? X69 ? X79 ? X89 = 0
XF1 ? X4F ? X8F ? X9F = 0
X12 ? 500 X15 ? 300 X16 ? 600
X23 ? 300 X24 ? 400
X34 ? 150
X48 ? 400 X4F ? 600
X57 ? 400
X67 ? 300 X69 ? 500
X76 ? 200 X79 ? 350
X84 ? 200 X89 ? 300 X8F ? 450
X98 ? 300 X9F ? 500
Xij ? 0 for all i and j
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______ conflict is centered on the personal relationship between group members.
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