The cost of operating the Maintenance Department is to be allocated to four production departments based on the floor space each occupies. Department A occupies $1000m^2$; Department $B,500m^2$; Department $C,1100m^2$; and Department $D,400m^2.$ If the July cost was $$42,000,$ how much of the cost of operating the Maintenance Department should be allocated to each production department?

The operating cost for Department $A$ is $

$($Simplify your answer.$)$