An animal breeder can buy four types of food for Vietnamese pot$-$bellied pigs. Each case of Brand A contains $35$ units of fiber, $40$ units of protein, and $40$ units of fat. Each case of Brand B contains $70$ units of fiber, $40$ units of protein, and $40$ units of fat. Each case of Brand C contains $105$ units of fiber, $40$ units of protein, and $50$ units of fat. Each case of Brand D contains $210$ units of fiber, $120$ units of protein, and $110$ units of fat. How many cases of each brand should the breeder mix together to obtain a food that provides $1890$ units of fiber, $920$ units of protein, and $1000$ units of fat?

Let $x$ represent the number of cases of Brand $A,y$ represent the number of cases of Brand $B,z$ represent the number of cases of Brand $C,$ and $w$ represent be the number of cases of Brand D$.$ There are four ways in which the breeder can mix brands to obtain a food that provides $1890$ units of fiber, $920$ units of protein, and $1000$ units of fat.

If $w=0,$ the solution is

$.$