Airport_Location - y 1.73 Distance from(0,y to(1,0 2 Therefore the three cities have the following coordinates City 1-1 City 2 1 City 3 1.73 Now

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Three cities are located at the vertices of an equilateral triangle. An airport is to be built at location that minimizes the total (straight-line) distance from the airport to the three cities.
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Problem 6.21 Airport Location Suppose two of the cities are at the coordinates (-1,0) and (1,0). Then clearly the first coordinate of the third city is 0. If y is its other coordinate (which we assume is positive), then since the triangle is equilateral, the distance from (0,y) to (1,0) must equal the distance from (-1,0) to (1,0), which is 2. We can use this fact to find y with the Goal Seek tool, using cell B9 as the changing cell to make the distance in cell B11 equal to 2.
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Unformatted text preview: y 1.73 Distance from (0,y) to (1,0) 2 Therefore, the three cities have the following coordinates: City 1-1 City 2 1 City 3 1.73 Now let the airport be at the point (x,y) x y Airport 0.58 Distances from airport to cities City 1 1.15 City 2 1.15 City 3 1.16 Total distance 3.46 Of course, the answer will depend on the way the coordinates of the 3 cities are chosen. The button is attached to a macro that runs the Solver with a different (randomly chosen) initial solution each time. It always gets the same final solution. A B C D E F G H I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29...
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This note was uploaded on 05/31/2009 for the course MBA 4500 taught by Professor Eyupcetin during the Spring '09 term at Istanbul Technical University.

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Airport_Location - y 1.73 Distance from(0,y to(1,0 2 Therefore the three cities have the following coordinates City 1-1 City 2 1 City 3 1.73 Now

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