Calculate the crude protein content of a feed mixture containing 91 kg of corn (8.0% CP) and 9 kg of urea (45% N). 2. Corrected_text: Calculate the nitrogen-free extract (NFE) in a feed which contains 11% water, 6% ash, 30% crude protein, 8% ether extract, and 5% crude fiber. 3. Corrected_text: If 2,000 IU of vitamin A is to be added per pound of feed, how much of vitamin A premix containing 2 million IU per pound should be added per ton (short ton)? 4. Corrected_text: Use the algebraic method to balance a crude protein supplement that contains 20% crude protein using wheat (11% CP) and safflower meal (SFM = 44% CP). 5. Corrected_text: Use the Pearson Square method to balance a protein supplement that contains 12% crude protein. Use corn (7.8% CP) and SBM (48% CP)
The Correct Answer and Explanation is:
Let’s go through each question one by one:
1. Crude Protein Content of a Feed Mixture
To calculate the crude protein content of the mixture, we need to find the total crude protein contributed by each ingredient and then divide by the total mass of the feed mixture.
Formula:
Crude Protein Content=Total Crude Protein from Corn+Total Crude Protein from UreaTotal Mass of Feed Mixture\text{Crude Protein Content} = \frac{\text{Total Crude Protein from Corn} + \text{Total Crude Protein from Urea}}{\text{Total Mass of Feed Mixture}}Crude Protein Content=Total Mass of Feed MixtureTotal Crude Protein from Corn+Total Crude Protein from Urea
Given:
- Corn = 91 kg, 8.0% CP
- Urea = 9 kg, 45% N (convert N to CP by multiplying by 6.25)
Calculation:
- Corn Crude Protein = 91×8.0100=7.28 kg91 \times \frac{8.0}{100} = 7.28 \, \text{kg}91×1008.0=7.28kg
- Urea Nitrogen = 9×45100=4.05 kg9 \times \frac{45}{100} = 4.05 \, \text{kg}9×10045=4.05kg N
Convert to CP: 4.05×6.25=25.31 kg CP4.05 \times 6.25 = 25.31 \, \text{kg} \, \text{CP}4.05×6.25=25.31kgCP - Total CP = 7.28+25.31=32.59 kg7.28 + 25.31 = 32.59 \, \text{kg}7.28+25.31=32.59kg
- Total Mass of Mixture = 91+9=100 kg91 + 9 = 100 \, \text{kg}91+9=100kg
Crude Protein Content = 32.59100×100=32.59%\frac{32.59}{100} \times 100 = 32.59\%10032.59×100=32.59%
2. Nitrogen-Free Extract (NFE)
NFE can be calculated as the difference between the total dry matter and the sum of other components. The formula is: NFE=100%−(Water %+Ash %+Crude Protein %+Ether Extract %+Crude Fiber %)\text{NFE} = 100\% – (\text{Water \%} + \text{Ash \%} + \text{Crude Protein \%} + \text{Ether Extract \%} + \text{Crude Fiber \%})NFE=100%−(Water %+Ash %+Crude Protein %+Ether Extract %+Crude Fiber %)
Given:
- Water = 11%
- Ash = 6%
- Crude Protein = 30%
- Ether Extract = 8%
- Crude Fiber = 5%
Calculation:
NFE=100%−(11%+6%+30%+8%+5%)=100%−60%=40%\text{NFE} = 100\% – (11\% + 6\% + 30\% + 8\% + 5\%) = 100\% – 60\% = 40\%NFE=100%−(11%+6%+30%+8%+5%)=100%−60%=40%
3. Vitamin A Premix
To find how much of the vitamin A premix to add per ton (short ton), we use the formula: Amount of premix (in pounds)=Desired IU×Total Feed Weight (in pounds)IU per pound of premix\text{Amount of premix (in pounds)} = \frac{\text{Desired IU} \times \text{Total Feed Weight (in pounds)}}{\text{IU per pound of premix}}Amount of premix (in pounds)=IU per pound of premixDesired IU×Total Feed Weight (in pounds)
Given:
- Desired IU = 2,000 IU per pound of feed
- Vitamin A Premix = 2 million IU per pound
- 1 ton = 2,000 pounds
Calculation:
Amount of premix=2,000×2,0002,000,000=2 pounds of premix per ton\text{Amount of premix} = \frac{2,000 \times 2,000}{2,000,000} = 2 \, \text{pounds of premix per ton}Amount of premix=2,000,0002,000×2,000=2pounds of premix per ton
4. Balancing a Crude Protein Supplement (Algebraic Method)
We are tasked with mixing wheat (11% CP) and safflower meal (44% CP) to make a 20% crude protein supplement. Let xxx be the amount of wheat (in kg) and yyy be the amount of safflower meal (in kg).
Equation setup:
0.11x+0.44y=0.20(x+y)0.11x + 0.44y = 0.20(x + y)0.11x+0.44y=0.20(x+y)
Simplifying:
0.11x+0.44y=0.20x+0.20y0.11x + 0.44y = 0.20x + 0.20y0.11x+0.44y=0.20x+0.20y 0.44y−0.20y=0.20x−0.11×0.44y – 0.20y = 0.20x – 0.11×0.44y−0.20y=0.20x−0.11x 0.24y=0.09×0.24y = 0.09×0.24y=0.09x xy=0.240.09=83\frac{x}{y} = \frac{0.24}{0.09} = \frac{8}{3}yx=0.090.24=38
Thus, for every 3 kg of safflower meal, we need 8 kg of wheat.
5. Balancing Protein Supplement (Pearson Square Method)
We are tasked with mixing corn (7.8% CP) and soybean meal (SBM = 48% CP) to create a 12% crude protein mixture.
Step 1: Draw the Pearson Square
- Place the target CP (12%) in the center.
- Place the CP of the ingredients (7.8% and 48%) on opposite corners.
Step 2: Subtract diagonally:
- 48−12=3648 – 12 = 3648−12=36 (amount of SBM)
- 12−7.8=4.212 – 7.8 = 4.212−7.8=4.2 (amount of corn)
Step 3: The ratio is 4.2 parts corn to 36 parts SBM.
Thus, the required amounts of corn and SBM can be mixed in this ratio to achieve the desired CP content.
