Problem $14-11($Algo$)$

DM Office Products $($DMOP$)$ is a wholesale supplier of office products with one facility in Pennsylvania. It

has decided to build a new distribution warehouse in the state of New York to help serve the growing

demand in that market. It has four major customers located in Buffalo, Syracuse, Albany, and New York

City. Though New York City is the largest market, it also has the greatest competition, and DMOP is not a

major player there. When DMOP ships an order to a customer, it uses its own small fleet of two trucks to

deliver, so the cost of delivery is essentially the same for a full or partially full truck. The expected

number of annual shipments to each city and their coordinates on an $x,y$ grid is shown in the following

table.

Use the centroid method to recommend a location for the new warehouse for DMOP.

Note: Round your answers to $1$ decimal place.DM Office Products $($DMOP$)$ is a wholesale supplier of office products with one facility in Pennsylvania. It has decided to build a new distribution warehouse in the state of New York to help serve the growing demand in that market. It has four major customers located in Buffalo, Syracuse, Albany, and New York City. Though New York City is the largest market, it also has the greatest competition, and DMOP is not a major player there. When DMOP ships an order to a customer, it uses its own small fleet of two trucks to deliver, so the cost of delivery is essentially the same for a full or partially full truck. The expected number of annual shipments to each city and their coordinates on an x$,$ y grid is shown in the following table.

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

Buffalo $35087588$

Syracuse $1,44592592$

Albany $2,325655132$

New York City $2,3005072$

Use the centroid method to recommend a location for the new warehouse for DMOP.