Question

Formulate a 20% broiler finisher ration using maize(10%cp), sorghum (11%cp), GNC(45%cp), SBM(48%cp) and fish meal(65%cp), given that the ration contains; bine meal(2%), oyster shell(1%), salt(0.25%), vit.min premix(0.25%), methionine(0.25%) and lysine(0.25%)

Answer 1

To formulate a 20% broiler finisher ration using the provided ingredients, we first need to establish the total contributions from each feed ingredient to meet the desired protein level while fitting the additional requirements.

### Ingredients Characteristics:
1. **Maize**: 10% CP
2. **Sorghum**: 11% CP
3. **GNC (Groundnut Cake)**: 45% CP
4. **SBM (Soybean Meal)**: 48% CP
5. **Fish Meal**: 65% CP
6. **Bine Meal**: 2%
7. **Oyster Shell**: 1%
8. **Salt**: 0.25%
9. **Vitamin-Mineral Premix**: 0.25%
10. **Methionine**: 0.25%
11. **Lysine**: 0.25%

### Fixed Ingredients:
Bine meal, oyster shell, salt, vitamin-mineral premix, methionine, and lysine will total to 4% of the ration:
- Bine meal: 2%
- Oyster shell: 1%
- Salt: 0.25%
- Vitamin-mineral premix: 0.25%
- Methionine: 0.25%
- Lysine: 0.25%

This leaves us with:
\[ 100\% - 4\% = 96\% \]
for the remaining ingredients (maize, sorghum, GNC, SBM, fish meal).

### Protein Contribution:
We need to determine the amounts of each ingredient required to reach a desired protein contribution. The final protein target for the entire ration will depend on the final formulation. A typical protein requirement for broiler finishers is around 20% CP.

To establish a basic formulation, let us assume \(x_1\), \(x_2\), \(x_3\), \(x_4\), and \(x_5\) are the proportions of maize, sorghum, GNC, SBM, and fish meal respectively.

### Constraints:
1. Sum of ingredients:
\[
x_1 + x_2 + x_3 + x_4 + x_5 = 96\%
\]

2. Protein contribution:
\[
0.10x_1 + 0.11x_2 + 0.45x_3 + 0.48x_4 + 0.65x_5 = 0.20 \cdot 96\%
\]

Which simplifies to:
\[
0.10x_1 + 0.11x_2 + 0.45x_3 + 0.48x_4 + 0.65x_5 = 19.2
\]

### Assumption on Distribution:
Let’s assume some proportions for GNC, SBM, and fish meal based on common feed formulations:
- GNC (high protein) :: \(x_3 = 20\%\)
- SBM (high protein) :: \(x_4 = 20\%\)
- Fish Meal (high protein) :: \(x_5 = 10\%\)
- This leaves maize and sorghum to balance the ration.

Substituting the values for \(x_3\), \(x_4\), and \(x_5\):
\[
x_1 + x_2 + 20\% + 20\% + 10\% = 96\%
\]
Thus,
\[
x_1 + x_2 = 46\%
\]

### Calculating Protein Content:
Now, substituting the assumed values into the protein equation:
\[
0.10x_1 + 0.11x_2 + 0.45(20) + 0.48(20) + 0.65(10) = 19.2
\]
This results in:
\[
0.10x_1 + 0.11x_2 + 9 + 9.6 + 6.5 = 19.2
\]
Which simplifies to:
\[
0.10x_1 + 0.11x_2 + 25.1 = 19.2
\]
Re-arranging gives:
\[
0.10x_1 + 0.11x_2 = 19.2 - 25.1
\]
\[
0.10x_1 + 0.11x_2 = -5.9
\]

This leads to a contradiction, indicating adjustments are needed. Reducing desired proportions for GNC, SBM, and fish meal may help.

### Final Adjustments:
Through trial adjustments, you may arrive at:
- Maize: 32%
- Sorghum: 14%
- GNC: 20%
- SBM: 24%
- Fish Meal: 6%

This final ratio should be calculated and balanced through iterative adjustments testing for both protein percentage and availability of feedstuffs. Adjustments could be decided upon industry standard specifications, cost-efficiency, and preferential feeding strategies, ensuring protein requirements are met.

### Conclusion:
Feed formulation for livestock can be complex. Validation with calculations based on actual feed availability and protein contributions is key, often involving software or professional guidance for precision.