A company wants to locate a distribution center that will serve six of its major customers in a 30 × 30 mi area. The locations of the customers relative to the southwest corner of the area are given in the following table in terms of (x, y) coordinates (the x direction is east; the y direction is north) (see Figure P28). Also given is the volume in tons per week that must be delivered from the distribution center to each customer. The weekly delivery cost ci for customer i depends on the volume Vi and the distance di from the distribution center. For simplicity we will assume that this distance is the straight-line distance. (This assumes that the road network is dense.) The weekly cost is given by ci = 0.5diVi, i = 1, …, 6.
Find the location of the distribution center (to the nearest mile) that minimizes the total weekly cost to service all six customers.
Figure P28
