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United Copiers sells and services copy machines to customers in 11 cities (Boston, Chicago, Dallas, Denver, Los Angeles, Miami, New York, Phoenix, Pittsburgh, San Francisco, Seattle) throughout the country. The company wants to set up service centers in three of these cities. The only potential service center locations are in Memphis, Houston, Cleveland, Buffalo, Minneapolis, St. Louis, and Kansas City. After United Copiers chooses the location of the service centers, it must assign customers in each city to one of the service centers. For example, if it decides to locate a service center in New York and then assigns its Boston customers to the New York service center, a service representative from New York will travel from Boston when ser- vices are required there. The distances (in miles) between the potential service center locations and the customer locations, and the estimated annual numbers of trips to the various customers are listed below. Boston Chicago Dallas Denver Los Angeles Miami New York Phoenix Pittsburgh San Francisco Seattle Memphis 1770 1694 319 2812 614 2542 2378 2977 1431 1302 978 Houston 1354 2115 1280 647 1471 2438 563 2859 2462 1421 1967 Cleveland Buffalo 615 1980 866 1155 2041 1187 2196 1451 2007 1813 1195 1831 1631 2450 1367 1230 1815 2678 317 1322 2746 836 Minneapolis 1035 1909 1369 2462 1072 420 2838 740 132 1762 540 St. Louis 1735 459 795 997 393 217 1881 1272 1788 941 851 Kansas City 1834 2405 1007 868 2053 383 1042 1216 1488 1656 1230 Expected #Trips 885 760 1124 708 1224 1152 1560 1222 856 1443 612 What should United Copiers do to minimize the total annual distance traveled by its service representatives?

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$5931

$6931

$5508

$6508

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