Rauschenberg Manufacturing is investigating which locations would best position
ID: 363934 • Letter: R
Question
Rauschenberg Manufacturing is investigating which locations would best position its new plant relative to three important customers (located in cities A, B, and C). As shown in the table below, all three customers require multiple daily deliveries. Management limited the search for this plant to those three locations and compiled the following information Location Coordinates (miles Deliveries per day (200,300) (400,200) (300,200) a. Which of these three locations yields the smallest total travel distance, based on Euclidean distances? Location yields the shortest travel transportation distance o miles. En er your repose de toned in a place.Explanation / Answer
We assume that the location of the new plant is at coordinate = 0, 0
Thus Eucledian distance between new plant and location A
= Square root ( ( 200 – 0 ) ^2 + ( 300 – 0 ) ^2 )
= Sqaure root ( 40,000 + 90,000)
= Square root ( 130,000)
= 360.55 miles
Therefore Total travel distance for location A
= The Eucledian distance as derived x Deliveries/ day
= 360.55 x 9 miles
= 3244.95 miles
Thus Eucledian distance between new plant and location B
= Square root ( ( 400 – 0 ) ^2 + ( 200 – 0 ) ^2 )
= Sqaure root ( 160000 + 40,000)
= Square root ( 200,000)
= 447.21 miles
Therefore Total travel distance for location B
= The Eucledian distance as derived x Deliveries/ day
= 447.21 x 5 miles
= 2236.05 miles
Thus Eucledian distance between new plant and location C
= Square root ( ( 300 – 0 ) ^2 + ( 200 – 0 ) ^2 )
= Sqaure root ( 90000 + 40,000)
= Square root ( 130,000)
= 360.55 miles
Therefore Total travel distance for location C
= The Eucledian distance as derived x Deliveries/ day
= 360.55 x 2
= 721.1 miles
Thus Location C yields smallest total travel distance based on Eucleidian distance
LOCATION C YILEDS THE SHORTEST TRAVEL ( TRANSPORTATION ) DISTANCE OF 721.1 MILES
LOCATION C YILEDS THE SHORTEST TRAVEL ( TRANSPORTATION ) DISTANCE OF 721.1 MILES
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