Suppose that a bus company is deciding where to locate its central hub. There are 6 possible destinations for the buses. Suppose that the center of town will be used as the reference for describing the possible destinations

Question

A is located 5 miles South and 3 miles West. B is located 3 miles North and 2 miles East. C is located 1 mile South and 5 miles East. D is located 2 miles North and 3 miles West. E is located exactly in the center of town. F is located 10 miles North and 5 miles East. Assume that traffic to each destination will be equal. Where should the hub go so that travel time is minimized?

Answer 1

Since each site has the same demand the coordinates can simply be averaged. Converting the center of town to (0,0 ) will mean that coordinates that are labeled South become -y and those labeled West become -x, while North becomes +y and East +x. Thus the location is found to be:
X = (-3 + 2 + 5 – 3 + 0 + 5 )/6 = 1
Y = (-5 + 3 – 1 + 2 + 0 + 10 )/6 = 1.5
Converting back into direction yields 1 mile East and 1.5 miles North of the center of town should be the location for the hub.