A company's disaggregation plan calls for the aggregate production to be broken down into $40$ percent Product A$,40$ percent Product B$,$ and $20$ percent Product C$.$ The aggregate plan calls for total production that averages $1,600$ units per quarter. Quarter $1$ production will be $800$ units, quarter $2$ production will be $1,400$ units, and quarter $3$ production will be $1,200$ units. How many units of Product A will be produced in quarter $4?$