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inventory at the beginning of the year. Determine the optimal production schedule for the four quarters to minimize total costs. 28. 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 trans- portation 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. Customer Location Freight Car Location 1. Portland A. Milwaukee B. Omaha C. Topeka D. Tucson E. Denver F. Wichita G. Minneapolis H. Memphis I. Kansas City Supply 27 23 23 26 21 29 40 45 23 1,100 31 26 22 20 34 47 43 26 720 38 31 18 24 27 51 48 34 1.450 2. Fresno 25 32 3. Long Beach 28 18 17 24 9 20 32 35 19 980 4. Salt Lake City 5. El Paso 41 27 24 11 18 22 46 30 25 650 6. Houston 38 24 22 16 27 25 41 28 23 1,025 7. St. Louis 15 14 10 27 23 12 19 10 9 1,330 12 13 15 31 26 17 14 15 14 1,275 8. Chicago Demand 974 1.225 1,690 710 1,261 663 301 479 1.227 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