# 100% original answers of the statistics questions.

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c. Application 11.2: Distance Measures
What is the distance between (20, 10) and (80, 60)?
Euclidean distance:
22
BABAAB
yyxxd
Rectilinear distance
BABAAB
yyxxd
Management is investigating which location would be best to position its new plant
relative to two suppliers (located in Cleveland and Toledo) and three market areas
(represented by Cincinnati, Dayton, and Lima). Management has limited the search
for this plant to those five locations. The following information has been collected.
Which is best, assuming rectilinear distance?
Location
(x, y) coordinates
Trips/year
Cincinnati
(11,6)
15
Dayton
(6,10)
20
Cleveland
(14,12)
30
Toledo
(9,12)
25
Lima
(13,8)
40
Calculations:
Cincinnati =
15( 0 ) + 20( 9) + 30(9) + 25(8) + 40(4)
=
Dayton =
15( 9) + 20( 0) + 30(10) + 25(5) + 40( 9)
=
Cleveland =
15(9) + 20(10) + 30( 0 ) + 25( 5) + 40(5)
=
Toledo =
15(8) + 20(5) + 30(5) + 25( 0 ) + 40(8)
=
Lima =
15(4 ) + 20(9) + 30(5) + 25(8) + 40( 0 )
=
So the best choice is shifting to Lima since it has the lowest total load distance.
Now how did I calculate all these? Note that in the above table in each row the values
without bracket is the trips per year of corresponding location and the values in the
bracket are the distances of that place from the shifted city (the corresponding city at the
1
st
column).

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﻿c. Application 11.2: Distance Measures What is the distance between (20, 10) and (80, 60)? Euclidean distance: Rectilinear distance d. Application 11.3: Load-Distance Method Management is investigating which location would be best to position its new plant relative to two suppliers (located in Cleveland and Toledo) and three market areas (represented by Cincinnati, Dayton, and Lima). Management has limited the search for this plant to those five locations. The following information has been collected. Which is best, assuming rectilinear distance? Location (x, y) coordinates Trips/year C ...
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