LOCATION STRATEGIES fixed costs in Dallas are lower due to cheaper land costs, but the variable costs in Dallas are higher because shipping distances would increase. Given the following costs: COST Fixed costs Variable costs DALLAS $600,000 $28/radio DETROIT $800,000 $22/radio a) Perform an analysis of the volume over which each location is preferable. b) How does your answer change if Dallas's fixed costs increase by 10%? PX ... 18 Hyundai Motors is considering three sites-A, B, and C-at which to locate a factory to build its new-model automo- bile, the Hyundai Sport C150. The goal is to locate at a minimum- cost site, where cost is measured by the annual fixed plus variable costs of production. Hyundai Motors has gathered the following data: SITE ANNUALIZED FIXED COST $10,000,000 $20,000,000 $25,000,000 VARIABLE COST PER AUTO PRODUCED $2,500 $2,000 $1,000 a) Near which map coordinates should the hub be located? b) If the shipments from city A triple, how does this change the coordinates? Px 21 A chain of home health care firms in Louisiana needs to locate a central office from which to conduct internal audits and other periodic reviews of its facilities. These facilities are scat- tered throughout the state, as detailed in the following table. Each team of workers, who will drive from the central office to the site. site, except for Houma, will be visited three times each year by a Houma will be visited five times a year. Which coordinates rep- resent a good central location for this office? What other factors might influence the office location decision? Where would place this office? Explain. Px CITY Covington Donaldsonville Houma Monroe Natchitoches MAP COORDINATES X y 9.2 3.5 7.3 2.5 7.8 1.4 5.0 8.4 2.8 6.5 5.5 2.4 5.0 3.6 3.8 8.5 23808588 27 5 25 5 you ABC The firm knows it will produce between 0 and 60,000 Sport C150s at the new plant each year, but, thus far, that is the extent of its knowledge about production plans. a) For what values of volume, V, of production, if any, is site Ca recommended site? b) What volume indicates site A is optimal? c) Over what range of volume is site B optimal? Why? Px 19 Peggy Lane Corp., a producer of machine tools, wants to move to a larger site. Two alternative locations have been identified: Bonham and McKinney. Bonham would have fixed costs of $800,000 per year and variable costs of $14,000 per standard unit produced. McKinney would have annual fixed costs of $920,000 and variable costs of $13,000 per standard unit. The finished items sell for $29,000 each. New Iberia Opelousas Ruston 22 A small rural county has experienced unprecedented growth over the past 6 years, and as a result, the local school dis- trict built the new 500-student North Park Elementary School. The district has three older and smaller elementary schools: Washington, Jefferson, and Lincoln. Now the growth pressure is being felt at the secondary level. The school district would like to build a centrally located middle school to accommodate students and reduce busing costs. The older middle school is adjacent to the high school and will become part of the high school campus. a) What are the coordinates of the central location? b) What other factors should be considered before building a school? PX 12 ods a) At what volume of output would the two locations have the same profit? 11 1200 10 North Park (500) 9 21200 b) For what range of output would Bonham be superior (have higher profits)? 8 7 c) For what range would McKinney be superior? d) What is the relevance of break-even points for these cities? PX 6 5 Highway Washington (200) bas boa 4 20 The following table gives the map coordinates and the shipping loads for a set of cities that we wish to connect through a central hub. 3 Jefferson (300) Lincoln (300) 2 CITY ABCDEFG 380 1 2 3 4 5 7 8 9 10 11 12 5 23 Todd's Direct, a major TV sales chain headquar tered in New Orleans, is about to open its first outlet in Mobile. Alabama, and wants to select a site that will place the new out- let in the center of Mobile's population base. Todd examines the seven census tracts in Mobile, plots the coordinates of the center of each from a map, and looks up the population base in each to use as a weighting. The information gathered appears in the following table. MAP COORDINATE (X, Y) SHIPPING LOAD (5, 10) 00 5 (6,8) 10 (4,9) 15 (9,5) (7,9) 15 (3,2) 10 (2,6) 5