In the half-ton batch example, how many pounds of soybean meal are needed to reach 15% CP?

In the half-ton batch example, how many pounds of soybean meal are needed to reach 15% CP?

• A. 857 lb
• B. 143 lb
• C. 100 lb
• D. 200 lb

Answer: (B)

To reach a specific crude protein level in a mixed feed, balance the protein from each ingredient so it meets the target for the whole batch. For a half-ton batch, assume 1000 lb total and a target of 15% crude protein, which means 150 lb of protein in the final mix. If corn has 10% CP and soybean meal has 45% CP, let x be the pounds of soybean meal used. The remaining weight is 1000 − x pounds corn. The protein contributed is 0.45x from soybean meal plus 0.10(1000 − x) from corn, and this must equal 150 lb: 0.45x + 0.10(1000 − x) = 150 0.45x + 100 − 0.10x = 150 0.35x = 50 x = 50 / 0.35 ≈ 142.86 lb So, about 143 pounds of soybean meal are needed to reach 15% CP in the 1000-lb batch.

To reach a specific crude protein level in a mixed feed, balance the protein from each ingredient so it meets the target for the whole batch. For a half-ton batch, assume 1000 lb total and a target of 15% crude protein, which means 150 lb of protein in the final mix.

If corn has 10% CP and soybean meal has 45% CP, let x be the pounds of soybean meal used. The remaining weight is 1000 − x pounds corn. The protein contributed is 0.45x from soybean meal plus 0.10(1000 − x) from corn, and this must equal 150 lb:

0.45x + 0.10(1000 − x) = 150

0.45x + 100 − 0.10x = 150

0.35x = 50

x = 50 / 0.35 ≈ 142.86 lb

So, about 143 pounds of soybean meal are needed to reach 15% CP in the 1000-lb batch.