Problem $1$

A company produces products A$,$ B$,$ and C$.$ The company can produce $1000L$ in any combination

of the three products so long as it produces $3L$ of product A for every $L$ of product $C$ it produces.

If product A sells for $9$ dollars per $L,$ product $B$ sells for $10$ dollars per $L,$ and product $C$ sells for

$11$ dollars per L$,$ what should the company produce in order to maximize its profits?