$[15$ points$]$ Following table shows location information and volume of shipped quantities from a

warehouse to several retail stores. Find the optimal location for the supply point using the centerof$-$gravity method. Show all calculations.

MGMT $3106$: Management Science and Operations Management

Retail

Outlet X coordinate Y coordinate Shipped

Quantity $($tons$)$

P $15102,000$

Q $25223,000$

R $5294,000$

S $1151,000$

T $23162,000$

U $18212,50$