The Sheridan Refining Company needs to locate an intermediate holding facility between its refining plant in Long Beach and its major distributors. We assume that inbound and outbound transportation costs are equal, and it does not include special shipping costs for less than full loads.

$($a$)$ Given the coordinate map and the amount of gasoline shipped to or from the plant and distributors, where is the centroid point? why? 

$($b$)$ What if we decrease the gallons shipped from Long Beach by the amount $“$Anaheim$”$ needs, and remove Anaheim from the calculations, and increase $“$LaHabra$”$ volume to $2000$ gallons per month Where would be the centroid point? Why?