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The following table shows the distances between three locations $($A$,$ B$,$ andC$)$ and the loads between three departments $($ X$,$ Y and Z$).$ The distances between locations are in kilometers Assume that the cost per kilometer to move any load is $$1.$ Design a facility location plan so that the total transportation cost is minimal. What is the total transportation cost for your design?

Locations

A

B

C

A

$60$

$80$

$70$

B

C

$60$

$80$

$70$

Departments

X

Y

X

$40$

$80$

Y

$60$

$30$

$50$

$20$

a $$45,000$

b$.$ $$19,500$

c$.$ $$17,500$

Q

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$22$