An animal breeder can buy four types of food for. Vietnamese pot$-$bellied pigs. Each case of Brand A contains $25$ units of fiber, $40$ units of protein, and $40$ units of fat. Each case of Brand B contains $100$ units of fiber, $130$ units of protein, and $120$ units of fat. Each case of Brand C contains $175$ units of fiber, $220$ units of protein, and $210$ units of fat. Each case of Brand D contains $300$ units of fiber, $390$ units of protein, and $350$ units of fat.How many cases of each brand should the breeder mix together to obtain a food that provides $3250$ units of fiber, $4150$ units of protein, and $3900$ units of fat?