A clothing manufacturer generates clothing in five locations in the U.S. In a move to vertical integration, the company is setting up a new fabric production plant that will supply fabric to all five clothing plants. The clothing plants have been positioned on a coordinate system as shown below:
Location X.Y
A 7, 2
B 4, 7
C 5, 5
D 6, 2
E 8, 4
a) If the shipments of fabric to each plant are equivalent, find out the optimal location for the fabric plant?
b) If the shipments of fabric to each plant vary per week as shown below: plant A, 200 units; plant B, 400 units; plant C, 300 units; plant D, 300 units; and plant E, 200 units, find out the optimal location for the fabric plant?