In a two$-$stage distribution system, there are three factories $($F$1,$ F$2,$ F$3)$ and three dealers $($D$1,$ D$2,$ D$3).$ A single product will be distributed in this system. Four

candidate central warehouse location sites $($CW$1,$ CW$2,$ CW$3,$ CW$4)$ are available.

It is decided to open at least two central warehouses. If CW$3$ is opened, then CW$2$ must not be opened. The demands of D$1,$ D$2$ and D$3$ are estimated as $15,000$

units, $6500$ units and $9000$ units, respectively. Other related data are provided below.

Construct the location$-$allocation model of the system $($Define the decision variables explicitly!$).$