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 c_i for customer i depends on the volume V_i and the distance d_i 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 c_i = 0.5d_iV_i, 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

Transcribed Image Text:

North 30 20 y (miles) 3 10 6 East 10 20 30 x (miles) 5, 4. 2.