Case 3: Krishna Copiers

Krishna Copiers sells and services copy machines to customers in 11 cities throughout the country. The company want to set up service centres in three of these cities. After Krishna Copiers chooses the location of the service centres, it must assign customers in each city to one of the service centres. For example, if it decides to locate a service centre in New York and then assigns its Boston customers to the New York service centre, a service representative from New York will travel from Boston when services are required there. The distances (in miles) between the cities are listed in the table below:

	Boston	Chicago	Dallas	Denver	LA	Miami	New York	Phoenix	Pittsburgh	San Francisco	Seattle
Boston	0	983	1815	1991	3036	1593	213	2664	792	2385	2612
Chicago		0	1205	1050	2112	1390	840	1729	457	2212	2052
Dallas			0	801	1425	1332	1604	1027	1237	1765	2404
Denver				0	1174	2041	1780	836	1411	1765	1373
LA					0	2757	2825	398	2456	403	1909
Miami						0	1258	2359	1250	3097	3389
New York							0	2442	386	3036	2900
Phoenix								0	2073	800	1482
Pittsburgh									0	2653	2517
San Fransisco										0	817
Seattle											0

The estimated annual number of trips to the various customer s are listed in the following table:

City	Annual Trips to Customers
Boston	885
Chicago	760
Dallas	1124
Denver	708
LA	1224
Miami	1152
New York	1560
Phoenix	1222
Pittsburgh	856
San Francisco	1443
Seattle	612

Develop and implement an LP solution, using binary variables that determines the locations of service centres and then assigns customers to these service centres to minimize the total annual distance travelled.