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clothing manufacturer produces clothing in five locations in the United States. In a move to vertical integration, the company is planning a new fabric production

clothing manufacturer produces clothing in five locations in the United States. 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 6, 2
E 8, 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 for the fabric plant?

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