CarMax is considering opening a new facility in Great Houston area to compete with local auto dealers. The current CarMax facilities are located at Humble, Katy, and Fresno. The location and sells per year are shown below with coordinates. Using a centroid method, determine the best location for the new facility. LOCATION COORDINATES Sells Per Year Humble 2200, 1500 1500 Katy 200, 800 800 Fresno 1500, 300 450 Using the centroid method, approximately what should the coordinates of the new facility be?

Question

Nicholas Mathis · Accepted Answer

The 3 points are   (  2200  ,  1500  )  ;  (  200  ,  800  )  ;  (  1500  ,  300  ) and the respective sales are 1500, 800 and 450.According to centroid method,  X-coordinate   =             Sum(X-coordinate of each point      ⋅       Sale)        Total sales    =            (      2200      ⋅      1500      +      200      ⋅      800      +      1500      ⋅      450      )              (      1500      +      800      +      450      )        =  1503.64  Y-coordinate   =            (      1500      ⋅      1500      +      800      ⋅      800      +      300      ⋅      450      )              (      1500      +      800      +      450      )        =  1100So the location for the new facility should be   (  1503.64  ,  1100  )