A clothing manufacturer produces clothing in five locations in the U. S. In a move to vertical integration, the company is planning a new fabric production plant that will supply fabric to all five clothing plants. The clothing plants have been located on a coordinate system as follows: Location (X, Y)
A 7,2
B 4,7
C 5,5
D 2,2
E 9,4
Shipments of fabric to each plant vary per week as follows: plant A, 200 units; plant B, 400 units; plant C, 300 units; plant D, 300 units; and plant E, 200 units. What is the optimal location of X for the fabric plant?

The optimal location of X for the fabric plant is 4.9

Explanation:      

    X    Y     W     X.W     Y.W

A   7    2     200   1400    400

B   4    7     400   1600    2800

C   5    5    300    1500    1500

D   2    2    300    600     600

E    9    4   200   1800     800

Total =      1,400  6,900  6,100

X= 6,900 / 1,400 = 4.9

Y= 6,100 / 1,400 = 4.4

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