Consider a location$-$allocation problem with three machines $($existing facilities$)$ located at the points $(0,0),(1,2)$ and $(2,1).$ It is anticipated that the number of times these machines are taken to a repair center in one planning period will be $10,5,$ and $15,$ respectively. Determine the number of repair centers $($new facilities$)$ and allocations of machines to these centers. Assume rectilinear distances, a cost of $$5$ per unit distance, and $$300$ as the cost of owning and operating each new facility during the planning period.