Rauschenberg Manufacturing is investigating which locations would best position

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) (200,100) 400,100) 200.200) Deliveries per day 8 a. Which of these three locations yields the smallest total travel distance, based on Euclidean distances? Location ? yields the shortest travel transportation) distance of miles. Enter your response rounded to one decimal place.

Explanation / Answer

Answer to question A :

Smallest total travel distance to a location should be defined as

= Deliveries per day x Square root ( X coordinate of the location^2 + Y coordinate of the location^2 )

Therefore ,

Smallest total travel distance to location A = 7 x Square root ( 200^2 + 100^2) = 7 x 223.60 =1565.20

Smallest total travel distance to location B = 3 x Square root ( 400^2 + 100^2) = 3 x 412.31 = 1236.93

Smallest total travel distance to location C = 4 x Square root ( 200^2 + 200^2 ) = 4 x 282.84 = 1131.36

LOCATION C YILEDS SHORTEST TRAVEL ( TRANSPORTATION ) DISTANCE OF = 1131.36 MILES

Answer to question B :

Let the coordinates of center of gravity = X, Y

Therefore

X x ( sum of deliveries per day ) = Sum of ( deliveries per day x X coordinate of location ) for 4 locations

Or , X x ( 7 + 3 + 4 ) =7 x 200 + 3 x 400 + 4 x 200

Or, 15.X = 1400 + 1200 + 800

Or, 15.X = 3400

Or, X = 226.7( ROUNDED TO 1 DECIMAL PLACE )

Similarly ,

Y X ( Sum of deliveries per day ) = sum of ( deliveries per day x Y coordinate of location ) for 4 locations

Or, Y x ( 7 +3 + 4 ) = 7 x 100 + 3 x 100 + 2 x 400

Or, 15.Y = 700 + 300 + 800

Or, 15.Y = 1800

Or, Y =120

CENTER OF GRAVITY : X = 226.7 MILES, Y = 120 MILES

LOCATION C YILEDS SHORTEST TRAVEL ( TRANSPORTATION ) DISTANCE OF = 1131.36 MILES

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