Distribution System

The Darby Company manufactures and distributes meter 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. A distribution center was established in Ft. Worth, Texas later, as business expanded to the north; 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; as a result, manufacturing costs are $.50 per meter less than at the El Paso plant. The company's rapid growth meant that not much attention was paid to the efficiency of the distribution system. Darby's management decided it is now 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 1 below. 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 Ft. 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 2.The cost per unit of shipping from each distribution center to each customer zone is given in Table 3. Note that some of the 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