SOLUTION: 4. A 200 lb batch of feed is being formulated using corn and soybean meal. The corn is 6.5% crude protein and the soybean meal is 45% crude protein. The final diet should be 15%

Question 204888: 4. A 200 lb batch of feed is being formulated using corn and soybean meal. The corn is 6.5% crude protein and the soybean meal is 45% crude protein. The final diet should be 15% crude protein. How much of each ingredient should be added to mix this batch of feed?
(HINT: Take x to be the lbs of corn and y to be the lbs of soybean meal. Develop two equations and solve them.)

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

OK, WE'LL FOLLOW THE HINT:
Let x=lbs of corn
And y=lbs of soybean meal
Now we are told that:
x+y=200-------------------------eq1
Now we know that the amount of pure crude protein before they are mixed (0.065x+0.45y) has to equal the amount of pure crude protein after they are mixed (0.15*200), so:
0.065x+0.45y=0.15*200 simplify
0.065x+0.45y=30------------------------eq2
Multiply eq1 by 0.065 (we get: 0.065x+0.065y=13) and then subtract it from eq2 and we get:
0.385y=17 divide each side by 0.385
y=44.2 lb ----------------------lbs of soybean meal needed
substitute y=44.2 into eq1:
x+44.2=200
x=200-44.2=155.8---------------lbs of corn needed
CK
0.065*155.8+0.45*44.2=0.15*200
10.1+19.9=30
30=30
Hope this helps---ptaylor

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