8. A company is performing a simplified analysis to determine approximately how far apart it should locate its warehouses. The company estimates that the fixed costs of operating a warehouse are $400,000 per year. It wants to determine how large an area to serve with the warehouse. The company estimates that 10 orders per year will be received per square mile served by the warehouse and that the shipping cost is $0.02 per mile for each order.

a. Begin with a 50-mile radius around the warehouse, and compute the number of orders to be served. Assume that each order in this circle will be shipped an average of 25 miles. Compute the total cost and cost per order in this 50-mile-radius area to be served by the warehouse.

b. Add a ring to the service area by extending the radius an additional 50 miles. Assume the order within this ring must be shipped an average of 75 miles. Compute the cost per order if the warehouse services a 100-mile radius.

c. Continue adding rings until you determine the radius at which the cost per order is minimized. What is the best radius?

d. In what ways would an actual analysis differ from the simplification used in this analysis?