PROBLEM 9 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 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 below: DISTRIBUTION CENTER PLANT El Paso San Bernardino Fort Worth 3.20 Santa Fe 2.20 3.90 Las Vegas 4.20 1.20 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 below: Customer Zone Dallas Demand (Meters) 6300 San Antonio 4880 Wichita 2130 Kansas City 1210 Denver 6120 Salt Lake City 4830 Phoenix 2750 Los Angeles 8580 4460 San Diego The cost per unit of shipping from each distribution center to each customer zone is given below; note that some distribution centers cannot serve certain customer zones. CUSTOMER ZONE DISTRIBUTION San Kansas Salt Lake Los San 0.3 CENTERS Dallas Antonio Wichita Fort Worth City Denver City Phoenix Angeles Diego 2.1 3.1 4.4 6.0 Santa Fe 5.2 5.4 4.5 6.0 2.7 4.7 3.4 3.3 2.7 Las Vegas 5.4 3.3 2.4 2.1 2.5 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 modified transportation model is used to minimize the cost of shipping from the production plants to the distribution centers.

PROBLEM 9 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 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 below: DISTRIBUTION CENTER PLANT El Paso San Bernardino Fort Worth 3.20 Santa Fe 2.20 3.90 Las Vegas 4.20 1.20 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 below: Customer Zone Dallas Demand (Meters) 6300 San Antonio 4880 Wichita 2130 Kansas City 1210 Denver 6120 Salt Lake City 4830 Phoenix 2750 Los Angeles 8580 4460 San Diego The cost per unit of shipping from each distribution center to each customer zone is given below; note that some distribution centers cannot serve certain customer zones. CUSTOMER ZONE DISTRIBUTION San Kansas Salt Lake Los San 0.3 CENTERS Dallas Antonio Wichita Fort Worth City Denver City Phoenix Angeles Diego 2.1 3.1 4.4 6.0 Santa Fe 5.2 5.4 4.5 6.0 2.7 4.7 3.4 3.3 2.7 Las Vegas 5.4 3.3 2.4 2.1 2.5 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 modified transportation model is used to minimize the cost of shipping from the production plants to the distribution centers.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

ChapterB: Differential Calculus Techniques In Management

Section: Chapter Questions

Problem 3E

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Variables
	Distribution centres
Plant	Fort Worth (3)	Santa Fe (4)	Las Vegas (5)
El Passo (1)	x₁₃	x₁₄	x₁₅
San Bernardino (2)	-	x₂₄	x₂₅

	Distribution Centers
	Dallas (6)	San Antonio (7)	Wichita (8)	Kansas City (9)	Denver (10)	Salt Lake City (11)	Phoenix (12)	Los Angeles (13)	San Diego (14)
Fort Worth (3)	x₃₆	x₃₇	x₃₈	x₃₉	x₃₁₀	-	-	-	-
Santa Fe (4)	x₄₆	x₄₇	x₄₈	x₄₉	x₄₁₀	x₄₁₁	x₄₁₂	x₄₁₃	x₄₁₄
Las Vegas (5)	-	-	-	-	x₅₁₀	x₅₁₁	x₅₁₂	x₅₁₃	x₅₁₄