The grid shows eight market locations to which a manufacturer of wooden windows

Question

The grid shows eight market locations to which a manufacturer of wooden windows expects to ship its products. The shipment volumes and X- and Y- coordinates of the locations are shown in the table. Using the center-of-gravity method, (a) find the Xc and Yc coordinates, and (b) suggest a possible warehouse location (10 Points) 3. MARKET AREA VOLUME Xi 8 2.5 Belfair Potlatch Oakland Atka Forks Highland Midvale Riverside 20 12 10 30 20 40 30 6.5 10 10 13 12 4 3.5 2 The fixed and variable costs for three potential manufacturing plant sites for a rattan chair weaver are shown (15 Points) 4. TFC: tvetme SITE FIXED COST PER YEAR VARIABLE COST PER UNIT $500 1,000 1,700 $11 7 4

Explanation / Answer

PLEASE FIND ANSWER TO QUESTION NUMBER 3 :

Let the coordinates of centralized location be ( Xc, Yc )

Accordingly,

Xc x Sum of all volumes = Sum of all ( Volume x Xi)

Or, ( 8 + 20 + 12 + 10 + 30 + 20 + 40 + 30 ) .Xc = ( 8 x 2.5 + 20 x 3 + 12 x 6.5 + 10 x 11 + 30 x 11 + 20 x 10 + 40 x 13 + 30 x 12 )

Or, 170.Xc = 20 + 60 + 78 + 110 + 330 + 200 + 520 + 360

Or, 170.Xc = 1678

Or, Xc = 1678 /170

Or, Xc = 9.87

Yc x sum of all volume = sum of all ( Volume x Yi )

Or, ( 8 + 20 + 12 + 10 + 30 + 20 + 40 + 30 ) .Xc = ( 8 x 2.5 + 20 x 3 + 12 x 6.5 + 10 x 11 + 30 x 11 + 20 x 10 + 40 x 13 + 30 x 12 )

Or, 170.Yc = ( 8 x 10 + 20 x 5 + 12 x 8 + 10 x 10 + 30 x 8 + 20 x 4 + 40 x 3.5 + 30 x 2 )

Or, 170.Yc = 80 + 100 + 96 + 100 + 240 + 80 + 140 + 60

Or, 170.Yc = 896

Or, Yc = 896 /170

Or, Yc = 5.27

THE ( Xc, Yc) coordinates are ( 9.87, 5.27)

Basis above coordinates of Xc, YC , in my opinion the central warehouse may be located at around Oakland or Atka

THE ( Xc, Yc) coordinates are ( 9.87, 5.27)

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