10.2. A temporary-help agency wants to open an office in a suburban section of a

Question

10.2. A temporary-help agency wants to open an office in a suburban section of a large city. It has identified five large corporate offices as potential customers. The loca- tions of these offices in miles on an xy coordinate grid for the area are ci = (4,4), c2 = (4, 11), c3 = (7, 2), C4 = (11, 11), and c5 = (14,7). The expected demand for temporary help from these customers is weighted as wi = 3, w2-2, w3-2, = 4, and w5-1 . The agency reimburses employees for travel expenses incurred by their assignments; therefore, recommend a location (i.e., xy coordinates) for the agency that will minimize the total weighted metropolitan distance for job-related travel

Explanation / Answer

The coordinates of the location of the office that minimizes the total weighted metropolitan travel distance can be determined by center of gravity method.

X coordinate = xi*wi / wi = (4*3+4*2+7*2+11*4+14*1)/(3+2+2+4+1) = 7.67

Y coordinate = yi*wi / wi = (4*3+11*2+2*2+11*4+7*1)/(3+2+2+4+1) = 7.417

Location of the central office = (7.67, 7.417)

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