HW12_sol

# HW12_sol - E160 Operations Research I Fall 2008 Homework#13...

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E160 Operations Research I Fall 2008 Homework #13 Solution Section 8.3 Problem 6 If the maximum flow = 21, then all packages can be loaded. Problem 8: See figure.

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Problem 16 All arcs from month i workers to Project j have a capacity of 6. All projects can be completed if and only if the maximum flow from source to sink equals 30. Section 8.5 Problem 4 a) All arcs have infinite capacity Arc Shipping Cost Bos-Chic 800 + 80 = \$880 Bos-Austin 800 + 220 = \$1,020 Bos-LA 800 + 280 = \$1,080 Ral-Chic 900 + 100 = \$1,000
Ral-Aus 900 + 140 = \$1,040 Ral-LA 900 + 170 = \$1,070 Chic-Aus \$40 Chic-LA \$50 Problem is balanced so no Dummy Point is needed City Net Outflow Boston 400 Raleigh 300 Chicago 0 LA -400 Austin -300 Problem 4b If at most 200 units can be shipped through Chicago, we must add a node Chicago'. Delete the Raleigh-Chicago and Boston- Chicago arcs and insert the following arcs Arc Shipping Cost Arc Capacity Boston-Chicago' \$880 Raleigh-Chicago' \$1000 Chicago-Chicago' 0 200 Review Section Problem 4

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Extra (which receives Total Supply-Total Demand) must be added so we know how much will be `shipped' out of each production point. Node Rt represents month t
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