Your boss has given you the task of recommending a location for a new warehouse in the country of Luxembourg. Your company is a wholesaler of fruit and needs to supply all of the stores of a major food chain in Luxembourg. Currently, all of the shipments of fruit comes out of the warehouse located in Germany and must travel into Luxembourg via the A1 motorway (interstate/autobahn), however, this road is often very busy and many delays typically occur. Therefore, to provide better customer service and reduce transportation costs and time the CEO wants to know where the best location in Luxembourg would be for a new warehouse.

You are provided a map of Luxembourg and the following daily shipment data by location. From this, you will need to calculate the best location based on the center-of-gravity approach.

Be as accurate as possible. If a location falls in the middle between the 1 and the 2 lines, you need to use 1.5 as your y or x location, (or 1.4 or 1.6 - whichever is closest).

Shipping Data

Town Apples Oranges Bananas

Clervaux 100 75 125

Wiltz 250 200 275

Vianden 200 150 225

Diekirch300 250 325

Ettelbruck 350 300 375

Echternach350300 375

Grevenmacher 300 250 350

Luxembourg 800700 900

Remich 200 150 250

Differdange150 100 150

Esch-sur-Alzette 250 200 225

Dudelange 200 200 200