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Demand Customer Zone Demand (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 If the current shipping rules are removed and any plant can supply any distribution center and then any customer zone (subject to not including the routes where costs were prohibitively high and not included in the tables), what is the minimum shipping cost for the next quarter? The Darby Company manufactures meters for measuring electric power consumption. The company has experienced rapid growth and has expanded to two manufacturing plants (El Paso and Sacramento) which ship to three distribution centers (Fort Worth, Santa Fe and Las Vegas) which then provide meters to nine customer zone warehouses (Dallas, San Antonio, Wichita, Kansas City, Denver, Salt Lake City, Phoenix, Los Angeles and San Diego) Each distribution center does NOT supply each customer zone. Data is provided below. Currently the plants and distribution centers have strict limits on service areas, with only one plant supplying a distribution center and only one distribution center supplies each customer zone. You have been brought in to make recommendations regarding the entire shipping system, from plant to customer zone (fractional decision solutions are acceptable). The cost to ship a meter from a plant to a distribution center is (note that not all of these routes are currently used). Distribution Center Plant Ft Worth Santa Fe Las Vegas El Paso $ 3.20 $ 2.20 $ 4.20 Sacramento $ 3.90 $ 1.20 Shipping from each distribution center to customer zone is (note that not all of these routes are currently used) (any routes without a cost are considered prohibitively expensive). Customer Zone Dist Ctr Dallas San Antonio Wichita Kansas City Denver Salt Lake City Phoenix Los Angeles San Diego Ft Worth $0.30 $ 2.10 $ 3.10$ 4.40 $ 6.00 Santa Fe $5.20$ 5.40 $ 4.50 $ 6.00 $ 2.70 $ 4.70 $ 3.40 $ 3.30$ 2.70 Las Vegas $ 5.40 $ 3.30 $ 2.40 $ 2.10 $ 2.50 Quarterly production capacity is 30,000 at El Paso and 20,000 at Sacramento Quarterly demands for meters are shown in the table below. Demand Customer Zone Demand (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 If the current shipping rules are removed and any plant can supply any distribution center and then any customer zone (subject to not including the routes where costs were prohibitively high and not included in the tables), what is the minimum shipping cost for the next quarter? The Darby Company manufactures meters for measuring electric power consumption. The company has experienced rapid growth and has expanded to two manufacturing plants (El Paso and Sacramento) which ship to three distribution centers (Fort Worth, Santa Fe and Las Vegas) which then provide meters to nine customer zone warehouses (Dallas, San Antonio, Wichita, Kansas City, Denver, Salt Lake City, Phoenix, Los Angeles and San Diego) Each distribution center does NOT supply each customer zone. Data is provided below. Currently the plants and distribution centers have strict limits on service areas, with only one plant supplying a distribution center and only one distribution center supplies each customer zone. You have been brought in to make recommendations regarding the entire shipping system, from plant to customer zone (fractional decision solutions are acceptable). The cost to ship a meter from a plant to a distribution center is (note that not all of these routes are currently used). Distribution Center Plant Ft Worth Santa Fe Las Vegas El Paso $ 3.20 $ 2.20 $ 4.20 Sacramento $ 3.90 $ 1.20 Shipping from each distribution center to customer zone is (note that not all of these routes are currently used) (any routes without a cost are considered prohibitively expensive). Customer Zone Dist Ctr Dallas San Antonio Wichita Kansas City Denver Salt Lake City Phoenix Los Angeles San Diego Ft Worth $0.30 $ 2.10 $ 3.10$ 4.40 $ 6.00 Santa Fe $5.20$ 5.40 $ 4.50 $ 6.00 $ 2.70 $ 4.70 $ 3.40 $ 3.30$ 2.70 Las Vegas $ 5.40 $ 3.30 $ 2.40 $ 2.10 $ 2.50 Quarterly production capacity is 30,000 at El Paso and 20,000 at Sacramento Quarterly demands for meters are shown in the table below