$[15$ 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

$\backslash$table$[[\backslash$table$[[$Retail$],[$Outlet$]],$X coordinate,Y coordinate,$\backslash$table$[[$Shipped$],[$Quantity $($tons$)]]],[$P$,15,10,2,000],[$Q$,25,22,3,000],[$R$,5,29,4,000],[$S$,11,5,1,000],[$T$,23,16,2,000],[$U$,18,21,2,500]]$