The National Western Railroad’s rail network covers most of the U.S. West and Midwest. On a daily basis it sends empty freight cars from various locations in its rail network to its customers for their use. Sometimes there are not enough freight cars to meet customer demand. The transportation costs for shipping empty freight cars, shown as follows, are directly related to distance traveled and the number of rail centers that must handle the car movement.

Determine the number of empty freight cars that should be sent from each rail network location to customers to meet demand at the minimum total cost.

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Customer Location Frelght Car Location A. Milwaukee B. Omaha C. Topeka D. Tucson E. Denver F. Wichlta G. Minneapolls H. Memphls 1. Kansas City Supply 1,100 720 1,450 27 31 38 23 26 31 23 25 32 26 22 18 21 20 24 29 34 27 40 47 51 45 43 48 23 26 34 I. Portland 2. Fresno 3. Long Beach 4. Salt Lake City 5. El Paso 6. Houston 7. St. Louis 28 18 17 24 20 32 35 19 980 41 38 15 27 24 14 13 24 22 18 27 23 26 22 25 12 17 30 28 10 15 25 23 650 1,025 1,330 1,275 46 16 27 31 41 19 14 10 8. Chicago 12 15 14 1,690 Demand 974 1,225 710 1,261 663 301 479 1,227