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The Darby Company manufactures and distributes meters used to measure electric power consumption. The company started with a small production plant...

What do I use for the coefficients when I plug the data into a Linear Program model?
The Darby Company manufactures and distributes meters used to measure electric power consumption. The company started with a small production plant in El Paso and gradually built a customer base throughout Texas. Adistribution center was established in Fort Worth, Texas, and later, as business expanded, a second distribution center was established in Santa Fe, New Mexico. The El Paso plant was expanded when the company began marketing its meters in Arizona, California, Nevada, and Utah. With the growth of the West Coast business, the Darby Company opened a third distribution center in Las Vegas and just two years ago opened a second production plant in San Bernardino, California. Manufacturing costs differ between the company’s production plants. The cost of each meter produced at the El Paso plant is $10.50. The San Bernardino plant utilizes newer and more efficient equipment; as a result, manufacturing costs are $0.50 per meter less than at the El Paso plant. Due to the company’s rapid growth, not much attention had been paid to the efficiency of the distribution system, but Darby’s management decided that it is time to address this issue. The cost of shipping a meter from each of the two plants to each of the three distribution centers is shown in Table 10.10. The quarterly production capacity is 30,000 meters at the older El Paso plant and 20,000 meters at the San Bernardino plant. Note that no shipments are allowed from the San Bernardino plant to the Fort Worth distribution center. The company serves nine customer zones from the three distribution centers. The forecast of the number of meters needed in each customer zone for the next quarter is shown in Table 10.11. The cost per unit of shipping from each distribution center to each customer zone is given in Table 10.12; note that some distribution centers cannot serve certain customer zones. In the current distribution system, demand at the Dallas, San Antonio, Wichita, and Kansas City customer zones is satisfied by shipments from the Fort Worth distribution center. In a similar manner, the Denver, Salt Lake City, and Phoenix customer zones are served by the Santa Fe distribution center, and the Los Angeles and San Diego customer zones are served by the Las Vegas distribution center. To determine how many units to ship from each plant, the quarterly customer demand forecasts are aggregated at the distribution centers, and a transportation model is used to minimize the cost of shipping from the production plants to the distribution centers. See attached jpeg for Network Model. Here is the result of using a linear program. What do I use as the coefficients when plugging into the LP? MIN 13.7EPFW + 12.7EPSF + 14.7EPLV + 13.9SBSF + 11.2SBLV + .3FWDA + 2.1FWSA + 3.1FWWI + 4.4FWKC + 6.0FWDE + 5.2SFDA + 5.4SFSA + 4.5SFWI + 6.0SFKC + 2.7SFDE + 4.7SFSL + 3.4SFPH + 3.3SFLA + 2.7SFSD + 5.4LVDE + 3.3LVSL + 2.4LVPH + 2.1LVLA + 2.5LVSD S.T. 1) EPFW + EPSF + EPLV < 30000 2) SBSF + SBLV < 20000 3) FWDA + FWSA + FWWI + FWKC + FWDE - EPFW = 0 4) SFDA + SFSA + SFWI + SFKC + SFDE + SFSL + SFPH + SFLA + SFSD - EPSF - SBSF = 0 5) LVDE + LVSL + LVPH + LVLA + LVSD - EPLV - SBLV = 0 6) FWDA + SFDA = 6300
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7) FWSA + SFSA = 4880 8) FWWI + SFWI = 2130 9) FWKC + SFKC = 1210 10) FWDE + SFDE + LVDE = 6120 11) SFSL + LVSL = 4830 12) SFPH + LVPH = 2750 13) SFLA + LVLA = 8580 14) SFSD + LVSD = 4460 Objective Function Value = 600942.000 Variable Value Reduced Costs -------------- --------------- ------------------ EPFW 14520.000 0.000 EPSF 6740.000 0.000 EPLV 0.000 0.000 SBSF 0.000 0.000 SBLV 20000.000 0.000 FWDA 6300.000 0.000 FWSA 4880.000 0.000 FWWI 2130.000 0.000 FWKC 1210.000 0.000 FWDE 0.000 0.000 SFDA 0.000 0.000 SFSA 0.000 0.000 SFWI 0.000 0.000 SFKC 0.000 0.000 SFDE 6120.00 0.000 SFSL 0.000 0.000 SFPH 0.000 0.000 SFLA 0.000 0.000 SFSD 620.000 0.000 LVDE 0.000 0.000 LVSL 4830.000 0.000 LVPH 2750.000 0.000 LVLA 8580.000 0.000 LVSD 3840.000 0.000
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