A 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: 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?

D) 5.6 , 4.4

Explanation:

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

we have to calculate the weighted average values for x and y to determine the optimal location of the new fabric production plant:

                     units     weight            weighted x     weighted y

plant A          200       0.143                  1.001               0.286              

plant B          400       0.286                 1.144               2.002

plant C          300       0.214                  1.07                1.07

plant D          300       0.214                  1.284              0.428

plant E          200       0.143                   1.144               0.572    

total              1,400      1                          5.643            4.358

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