4. (10pts)A network of railway lines connects the main lines entering and leavin

Question

4. (10pts)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 train cars can pass per hour. Formulate an LP model to find the maximal flow in train cars per hour from Node 1 to Node F. (Only interested in the LP model. You are NOT required to solve it with Lingo or Solver) where the numbers represent how 400 300 150 400 600 500 200 450 600 300 300 300 500 400 300 350

Explanation / Answer

Maximum =1F

subject to constraint

X12<500

X15<300

X16<600

X23<300

X24<400

X34<150

X48<400

X57<400

X67<300

X69<500

X76<200

X79<350

X84<200

X89<300

X98<300

X4F<600

X8F<450

X9F<500

X12,X15,X16,X23,X24,X34, X48,X57,X67,X69,X76,X79,X84,X89,X98,X4F,X8F,X9F>6750

Calculation

500+300+600+300+400+150+400+400+300+500+200+350+200+300+300+600+450+500=6750

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