Question

All values are on an "as-fed" basis wheat 12% moisture, 14.5% CP, 0.39% Lysine Soybean meal: 11% moisture, 47.7% CP, and 2.96% Lysine Peanut meal: 8% moisture, 45.5% CP, and 1.44% Lysine 1. Calculate CP and Lys concentrations (DM-basis) for all ingredients Note: use the as-is values reported above for the exercises below 2. Use algebraic equations to formulate a 23% CP mixture containing only wheat and soybean meal. 3. Use Pearson Square method to do the same.

Answer 1

Concentrations are given as-fed basis which includes moisture.

1- If 12% is the moisture in wheat, that means that 88% is dry material (DM). So in order to get concentrations in DM  basis, you need to divide the original results in by the DM

Wheat: 14.5/0.88=16.48% CP and 0.39/0.88=0.44% Lys

For soybean, 11% is the moisture and 89% DM

Soybean: 53.59% CP and 3.33% Lys

Peanut has 8% moisture and therefore 92% DM

Peanut 49.02% CP and 1.57% Lys

2- If you need a final concentration of 23% CP (this means that in 100 kg of meal you have 23 kg of CP). These 100 kg final meal consists of wheat and soybean in different proportions.

Let's use X1 for the kgs of wheat needed to prepare 100kg final meal and X2 for the kgs of soybean needed to prepare 100kg final meal. Then X1+X2=100, and X2=100-X1

23 kg CP= X1*0.145 + X2*0.477

Replace X2 by the formula X2=100-X1

0.145X1 + (100-X1)0.477 = 23

0.145X1 + 47.7 -0.447X1=23

47.7-23 = 0.332X1

X1= 24.7/0.332= 74.39 Kg of wheat

X2= 100-X1= 26.61 Kg of soybean

3-

PEAR SON SQUARE WHEAT 4.S WHEAT 23) CP SO4B EA CP 33.2 TOTAL PARTSs