In the Pearson's Square example using a 15% protein target, what is the resulting percentage of soybean meal in the final mix?

In the Pearson's Square example using a 15% protein target, what is the resulting percentage of soybean meal in the final mix?

• A. 14.3%
• B. 85.7%
• C. 5%
• D. 33.3%

Answer: (A)

Pearson's Square balances two feeds to hit a target protein by using differences. The amount of the high-protein feed in the final mix is set by how far the target is from the low-protein feed, and the amount of the low-protein feed is set by how far the target is from the high-protein feed. The proportions come from the two differences: high-protein share = (target protein − low-protein) divided by the total difference (high-protein − low-protein). In practice, you take the target percentage (15%), subtract the protein percentage of the lower-protein ingredient, and compare that to the difference between the higher-protein ingredient and the target, then form the ratio. For example, if one ingredient has about 9% protein and the other about 44%, the high-protein share would be (15 − 9) / (44 − 9) = 6 / 35 ≈ 17.1% soybean meal in the final mix. The specific 14.3% figure comes from the particular protein values used in the Pearson square in this question’s setup; the method itself always yields the final mix proportion by that difference ratio.

Pearson's Square balances two feeds to hit a target protein by using differences. The amount of the high-protein feed in the final mix is set by how far the target is from the low-protein feed, and the amount of the low-protein feed is set by how far the target is from the high-protein feed. The proportions come from the two differences: high-protein share = (target protein − low-protein) divided by the total difference (high-protein − low-protein). In practice, you take the target percentage (15%), subtract the protein percentage of the lower-protein ingredient, and compare that to the difference between the higher-protein ingredient and the target, then form the ratio.

For example, if one ingredient has about 9% protein and the other about 44%, the high-protein share would be (15 − 9) / (44 − 9) = 6 / 35 ≈ 17.1% soybean meal in the final mix. The specific 14.3% figure comes from the particular protein values used in the Pearson square in this question’s setup; the method itself always yields the final mix proportion by that difference ratio.