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 $50$ units of fiber, $40$ units of protein, and $30$ units of fat. Each case of Brand $C$ contains $75$ units of fiber, $40$ units of protein, and $40$ units of fat. Each case of Brand D contains $100$ units of fiber, $80$ units of protein, and $40$ units of fat. How many cases of each should the breeder mix to obtain a food that provides $1350$ units of fiber, $880$ units of protein, and $760$ units of fat? be the number of cases of Brand $C,$ and $w$ be the number of cases of Brand $D.$ Choose the correct answer below.

A$.$

$25x+50y+75z+100w=1350$

$40x+40y+40z+80w=880$

$40x+30y+40z+40w=760$

c$.$

$25x+50y+75z+100w=880$

$40x+40y+30z+80w=1350$

$75x+40y+40z+40w=760$

Select all that apply.

A$.1$ brand $A,8$ brand $B,11$ brand C$,1$ brand D

C$.2$ brand A$,4$ brand B$,12$ brand C$,2$ brand D

E$.4$ brand $A,0$ brand $B,12$ brand $C,0$ brand $D$

G$.5$ brand A$.12$ brand B$.4$ brand C$.0$ brand D

B$.$

$25x+50y+75z+100w=1350$

$40x+40y+40z+80w=880$

$40x+40w=760$

D$.$

$25x+50y+75z=760$

$40x+40y+80w=880$

$40x+30y+40z+40w=1350$

B$.0$ brand $A,0$ brand $B,10$ brand $C,12$ brand $D$

D$.3$ brand A$,0$ brand $B,13$ brand C$,3$ brand D

F$.2$ brand A$,4$ brand B$,2$ brand C$,12$ brand D

H$.0$ brand A$.12$ brand B$.10$ brand C$.0$ brand D