1. The Census Problem Location on a plane Turn-in Problem #10

2. The Problem BuyItHere.com plans to produce and sell a variety of merchandise over the internet. Items will be produced and stored in a single collocated factory / warehouse and shipped to customers free of charge. Since BuyItHere must absorb the shipping expense, they would like to keep their distribution costs to a minimum. Therefore, they wish to “centrally” locate their warehouse.

3. The Data The data identifying the largest 195 metropolitan areas in the US was compiled from the 2000 Census by an engineer manager in support of this activity. RankMetropolitan AreaPopulationdegreesmin Ndegreesmin W 1 New York--Northern New Jersey--Long Island 21,199,8654042.5740 2 --Riverside-- County, CA 16,373,645343.511815 3 Chicago----, IL--IN--WI 9,157,540407.18814.6 4 Washington-- --MD--VA--WV 7,608,0703853.3772 5 San Francisco--Oakland--San Jose 7,039,3623746.512225 6 Philadelphia--Wilmington-- Atlantic City 6,188,4633957759.8 7 Boston--Worcester--Lawrence 5,819,1004221.7713.5 8 Detroit--Ann Arbor--Flint, MI 5,456,4284220833 Source: Population Division, U.S. Census Bureau

4. The Analysis Determining the location of the factory / warehouse under the following conditions. For parts a. and b., assume that the amount of items shipped to each location in the attachment is proportional to its population. a.The majority of the items are to be shipped via UPS where the cost is proportional to the “straight-line” distance. b.The majority of the items are to be shipped by the company’s own fleet of trucks in which case they will primarily use the (rectilinear) interstate system of North-South and East-West roads. c.The company desires to locate where the maximum straight-line distance to any of the major population areas is minimized. This will then minimize the maximum delivery cost incurred. d.The company desires to locate where the maximum rectilinear (driving) distance to any of the major population areas is minimized. e.Repeat c. with metropolitan areas in Hawaii and Alaska omitted. f.Repeat d. with metropolitan areas in Hawaii and Alaska omitted.

5. Simply complete the following table: decimal latitude decimal longitude nearest city/town a. b. c. d. e. f. Note: Solutions will be submitted via a web submission form found on the course website.