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. A distribution center was established in Fort Worth, Texas and later, as bsuiness 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 AZ, CA, NV, and UT. 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, CA. 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 new and more efficient equipment; as a result, manufacturing costs are $0.50 per meter less than at El Paso Plant. Due to the company's rapid growth, not much attention had been paid to the efficiency of its supply chain, 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 below: El Paso to Fort Worth 3.20, El Paso to Santa Fe 2.20, El Paso to Las Vegas 4.20 San Bernardino to Fort Worth --, San Bernardino to Santa Fe 3.90, San Bernardino to Las Vegas 1.20 The quarterly production capacity is 30,000 meters at El Paso 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 below. Customer Zone/Demand in meters Dallas 6300 San Antonio 4880 Wichita 2130 Kansas City 1210 Denver 6120 Salt Lake City 4830 Phoenix 2750 Los Angeles 8580 San Diego 4460 The cost per unit of shipping from each distribution center to each customer zone is given below. Note that some distribution centers cannont serve certain customer zones. These are indicated by a dash. Fort Worth, Dallas (0.3), San Antonio (2.1), Wichita (3.1), Kansas City (4.4), Denver (6.0), Salt Lake City (-), Phoenix (-), Los Angeles (-), San Diego (-) Santa Fe, Dallas (5.2), San Antonio (5.4), Wichita (4.5), Kansas City (6.0), Denver (2.7), Salt Lake City (4.7), Phoenix (3.4), Los Angeles (3.3), San Diego (2.7) Las Vegas, Dallas (-), San Antonio (-), Wichita (-), Kansas City (-), Denver (5.7), Salt Lake City (3.3), Phoenix (2.4), Los Angeles (2.1), San Diego (2.5) In its current supply chain, demand at the Dalls, 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. 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 minimze the cost of shipping from the poduction plants to the distribution centers. QUESTIONS - PLEASE SHOW WORK AND PROVIDE EXPLANATION

1) If the company does not change its current supply chain, what will its distribution costs be for the following quarter?

2) Suppose that the company is willing to consider dropping the distribution center limitations; that is, customers could be served by any of the distribution centers for which costs are available. Can costs be reduced? If so, by how much?

3)The company wants to explore the possibility of satisfying some of the customer demand directly frrom the prodcution plants. In particular, the shipping cost is $0.30 per unit from San Bernardino to Los Angeles and $0.70 from San Bernardino to San Diego. The cost for direct shipments from El Paso to San Antonio is $3.50 per unit. Can distribution costs be further reduced by considering these direct plant-to-customers shipments?

4) Over the next five years, Darby is anticipating moderate growth (5000 meters) to the north and west. Would you recommend that Darby consider plant expansion at this time?