The Natural Berry Beverage Company is known for their natural berry flavored bottled soft drinks delivered to the Western United States. The company's products are enjoying a growing reputation and increased demand throughout the American Southwest. Because of the high cost of transporting soft drinks, they are considering a new plant to serve the states of Texas and Oklahoma. A key concern in their search for a new location is the resultant transportation costs to serve their key markets. Following is a list of cities where their main wholesale customers are located, along with estimated annual demand in cases of product for each.

CITY x$-$COORDINATES y$-$COORDINATES NUMBER OF CASES

Phoenix $25025025,000$

Tucson $35012520,000$

Albuquerque $80045023,000$

Santa Fe $85052017,000$

a$.$ Use the centroid method to recommend a location for the new bottling plant.