A textile factory produces men€™s clothes at the following five locations in Southern India: Tirunelveli, Palakad, Tiruppur, Tumkur, and Vijayawada. The company now needs to determine the best location to distribute bolts of cloth to the five manufacturing locations. The map coordinates of the five manufacturing locations and the weekly quantity to be shipped to each of the five locations are given in the following table:

1. Determine the best location for the distribution center using the center-of gravity method.

2. Based on your answer to part a), identify the closest town to the map coordinates to locate the distribution center.

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Manufacturing Location Map Coordinates (x, y) (15, 5) (5, 20) (10, 25) (8, 35) (35, 70) Weekly Shipment Quantity (in bolts) Tirunelveli Palakad 20 25 Tiruppur 45 Tumkur 30 35 Vijayawada