In the Pearson's Square example to make 13% CP using 32.8 parts of corn at 8.9% CP and 45.8% CP SBM, how many parts of SBM are needed?

In the Pearson's Square example to make 13% CP using 32.8 parts of corn at 8.9% CP and 45.8% CP SBM, how many parts of SBM are needed?

• A. 0.5
• B. 8.2
• C. 4.1
• D. 12.0

Answer: (C)

To hit a target CP with two feeds, you compare how far the target is from each feed’s CP and use those differences to set the mixing ratio. The feed with the higher CP (soybean meal at 45.8%) pulls the mix up toward 13%, while the lower-CP feed (corn at 8.9%) pulls it down. Calculate the differences: 45.8 minus 13 equals 32.8, and 13 minus 8.9 equals 4.1. The amount of low-CP corn you need is proportional to the larger difference (32.8), and the amount of high-CP SBM you need is proportional to the smaller difference (4.1). So the SBM to corn ratio is 4.1 to 32.8, or SBM is 0.125 times the amount of corn. If corn is 32.8 parts, SBM should be 0.125 × 32.8 = 4.1 parts. You can also confirm algebraically by solving (0.089 × 32.8 + 0.458 × x) / (32.8 + x) = 0.13, which gives x = 0.125 × 32.8 = 4.1.

To hit a target CP with two feeds, you compare how far the target is from each feed’s CP and use those differences to set the mixing ratio. The feed with the higher CP (soybean meal at 45.8%) pulls the mix up toward 13%, while the lower-CP feed (corn at 8.9%) pulls it down.

Calculate the differences: 45.8 minus 13 equals 32.8, and 13 minus 8.9 equals 4.1. The amount of low-CP corn you need is proportional to the larger difference (32.8), and the amount of high-CP SBM you need is proportional to the smaller difference (4.1). So the SBM to corn ratio is 4.1 to 32.8, or SBM is 0.125 times the amount of corn.

If corn is 32.8 parts, SBM should be 0.125 × 32.8 = 4.1 parts. You can also confirm algebraically by solving (0.089 × 32.8 + 0.458 × x) / (32.8 + x) = 0.13, which gives x = 0.125 × 32.8 = 4.1.