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

$(300,300)$

$9$

B

$(400,200)$

$8$

C

$(200,200)$

$7$

Part $2$

a$.$ Which of these three locations yields the smallest$$ load$-$distance score, based on Euclidean$$ distances?

Location

$$

B

A

C

yields the smallest$$ load$-$distance score of $$enter your response here. $($Enter your response rounded to one decimal$$ place.$)$

Part $3$

b$.$ Which of these locations is$$ best, based on rectilinear$$ distances?

Location

$$

A

B

C

is the$$ best, yielding a$$ load$-$distance score of $$enter your response here. $($Enter your response as a whole$$ number.$)$

Part $4$

c$.$ What are the coordinates of the center of$$ gravity?

The center of gravity is x$*=$enter your response here $$miles$,$ y$*=$enter your response here miles. $($Enter your responses rounded to one decimal$$ place.$)$