Answered: The distance between two cities in the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

The distance between two cities in the United States can be approximated by the following formula, where lat₁ and long₁ are the latitude and longitude of city 1 and lat₂ and long₂ are the latitude and longitude of city 2.

(lat₁ − lat₂)² + (long₁ − long₂)²

Ted's daughter is getting married, and he is inviting relatives from 15 different locations in the United States. The file Wedding gives the longitude, latitude, and number of relatives in each of the 15 locations.

Ted would like to find a wedding location that minimizes the demand-weighted distance, where demand is the number of relatives at each location. Assuming that the wedding can occur anywhere, find the latitude and longitude of the optimal location. (Hint: Notice that all longitude values given for this problem are negative. Make sure that you do not check the option for Make Unconstrained Variables Non-Negative in Solver. Round your answers to three decimal places.)

latitude of the optimal wedding location:

longitude of the optimal wedding location:

Location
lat
long
# Relatives
New York
40.7143528
-74.0059731
43
Maryland
39.0256651
-77.0763669
8
Virginia
37.4315734
-78.6568942
2
SC
32.2163160
-80.7526080
1
NC
35.7720960
-78.6386145
12
TN
35.9606384
-83.9207392
1
FL
27.4989278
-82.5748194
Ohio
39.1361110
-84.5030556
Wyoming
43.6226250
-110.6260590
1
CA
34.0194543
-118.4911912
10
Iowa
41.6986111
-93.0469444
7
IL
41.8500330
-87.6500523
4
Mass
42.9339792
-70.7983855
1
NJ
40.9012101
-74.5143232
10
PA
39.9523350
-75.1637890
2

1 Location
2 New York
3 Maryland
4 Virginia
5 SC
lat
long
# Relatives
40.714
-74.006
43
39.026
-77.076
8
37.432
-78.657
32.216
-80.753
1
6 NC
7 TN
35.772
-78.639
12
35.961
-83.921
8 FL
27.499
-82.575
9 Ohio
10 Wyoming
11 CA
12 Iowa
13 IL
14 Mass
15 NJ
39.136
-84.503
6.
43.623
-110.626
1
34.019
-118.491
10
41.699
-93.047
7
41.850
-87.650
4
42.934
-70.798
1
40.901
-74.514
10
16 PA
39.952
-75.164
17
1.
2.

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