A clothing retailer is trying to decide where to locate a warehouse that will supply their six locations. They create a map and place their first location (location A) at position (0,0) on the map. Then add

the coordinates of the other locations based on that. For example, location B is 10 miles east and 15

miles north of location A, so it’s placed at (10,15). Each retailer will need a differing number of

shipments from the warehouse per year. The coordinates for the retailers and number of shipments

required is provided by the table below:

Location x-coord y-coord # of shipments

A 0 0 10

B 10 15 15

C 2 12 12

D 8 4 8

E 4 2 10

F 3 6 5

a. (2 pts) Where should they locate the warehouse to minimize the total distance shipments to the

retailers will have to travel? Assume for this part that the shipments can travel in a straight line

directly from the warehouse to the retailer.

Hint: The Pythagorean theorem states that the distance between two points is

√(1 − 0

)

2 + (1 −

)

2

b. (1 pt) Now assume that zoning ordinances prevent them from placing the warehouse within 5

miles of locations D or F. Where should they place the factory in order to minimize distance?

c. (2 pts) Ignore the restriction from part (b) for this question. Suppose the retail locations and the

factory are in a city whose streets are arranged in a grid. For example, to get from Location A to

Location B, one would travel a total of 25 miles (10 over then 15 up). Where should they locate

their warehouse?​