Rauschenberg Manufacturing is investigating which locations would best position
ID: 1997252 • 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
A
(200,100)
5
B
(500,200)
7
C
(300,300)
9
a. Which of these three locations yields the smallest total travel distance, based on Euclidean distances?
Location (A,B,C) yields the shortest travel (transportation) distance of ____miles. (Enter your response rounded to one decimal place.)
b. Which of these locations is best, based on rectilinear distances?
c. What are the coordinates of the center of gravity?
Explanation / Answer
a) if we choose A
euclidean distance between A and B = 500,200 - 200,100 = 300,100
no of deliveries = 7 so total distance for B = 2100,700
euclidean distance between A and C = 300,300 - 200,100 = 100,200
no of deliveries = 9 so total distance for C = 901800
total travel= 2100,700 + 901800 = 3002500
if we choose B
uclidean distance between A and B = 500,200 - 200,100 = 300,100
no of deliveries = 5 so total distance for B = 1500,500
euclidean distance between B and C = 500,200 - 300,300 = 199900
no of deliveries = 9 so total distance for C = 1799100
total travel= 3299600
IF WE CHOOSE C
euclidean distance between A and C = 300,300 - 200,100 = 100,200
no of deliveries = 5 so total distance for A = 501000
euclidean distance between B and C = 500,200 - 300,300 = 199900
no of deliveries = 7 so total distance for B = 1399300
TOTAL DISTNCE = 1900300
b)
SO OBVIOUSLY C IS THE BEST CHOICE
c)centre of gravity
= ( 5 * 200100 + 7 * 500200 + 9 * 300300) / (5+7+9) = 343076.19
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