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The San Marcau Company produces 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 San Marcau 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 $11.50. The San Bernardino plant utilizes new
and more efficient; as a result, manufacturing costs are $.50 per meter
less than at the El Paso plant.
The company’s rapid growth meant that not much attention was paid to
the efficiency of the distribution system. But, San Marcau’s management
decided it is now time to address this issue. The cost of shipping a
meter from each of the two plants to each of the three distribution
centers is shown in Table 1 below.
Table 1 Shipping cost per unit ($) from production plants to distribution centers
Plant Ft Worth Sante Fe Las Vegas
El Paso 3.00 2.20 4.20
San Bernardino — 3.90 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 Ft. Worth
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.
Table 2: Quarterly Demand Forecast
Customer Zone Demand (meters)
San Antonio 4880
Kansas City 1210
Salt Lake City 4830
Los Angeles 8580
San Diego 4460
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.
Table 3: Shipping cost from distribution centers to customer zones ($)
Dallas San Antonio Wichita Kansas City Denver Salt Lake City Phoenix LA SD
Ft Worth 0.3 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 2.0 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 Ft. Worth distribution center. In a similar manner,
the Denver, Salt Lake City, and Phoenix customer zones are served by the
Santa Fe distribution, 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
1. If the company does not change its current distribution strategy,
what will its manufacturing and distribution costs be for the following
2. Suppose that the company is willing to consider dropping the
distribution center limitations; that is, customer could be served by
any of the distribution centers for which costs are available. Can costs
be reduced? By how much?
Please show ALL work.