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?