<p> RECTILINEAR DISTANCE LOCATION PROBLEMS</p><p>1. Mr. J has to pick up various items from 5 locations in downtown Springfield for his next business trip. He wants to find a parking space that will minimize the distance he has to walk to visit all 5 locations without re-parking. Each block is a square, one quarter mile on each side. Streets running north-south are numbered consecutively. Streets running east-west are lettered consecutively. The locations he must visit are at the following 5 intersections: F and 9th, C and 6th, E and 7th, G and 5th and E and 3rd. He must make two trips to E and 3rd because he can not carry everything in one load. The other locations require a single visit. Mr. J must stay on the sidewalks that enclose each block and the distance required to cross the street is considered negligible. a) Where should Mr. J park his car? b) If there is no parking on D, E and F Streets, where should Mr. J park? </p><p>2. The KB Computer Company has 10 stores in Nashville. A new warehouse is needed to service these stores. The store locations and deliveries per week are: </p><p>Store Location (miles) Demand (deliveries per week) 1 (2,0) 3 2 (2,6) 1 3 (4,3) 2 4 (1,-2) 2 5 (-2,0) 2 6 (-2,1) 1 7 (-4,5) 5 8 (-3,-4) 5 9 (-6,-2) 2 10 (-1,5) 4 </p><p>Assume that travel is on a rectangular grid of streets. a) Where should the warehouse be located to minimize the total distance for deliveries? b) What is the total distance traveled for deliveries each week? c) If the warehouse must be at least 2 (rectangular) miles from all stores, where should it be located to minimize the total distance for deliveries? </p><p>Note that the points (0,2), (0.5,1.5), (0.6,1.4), (1,1) and (2,0) are all 2 miles from the point (0,0). </p>