1. Simultaneous Equations Diet Balancing

2. Simultaneous Equations Used to balance for 2 nutrients Usually protein and energy Balances for required amounts Lb, kg, or Mcal Uses 2 ingredients or 2 mixtures of ingredients

3. Simultaneous Equations Identify feeds and their composition Feed A – 10% CP, 80% TDN Feed B – 35% CP, 50% TDN

4. Simultaneous Equations Identify animal requirements 0.8 lb CP and 4.0 lb TDN per day Let A = lb of Feed A needed Let B = lb of Feed B needed

5. Simultaneous Equations Lb Feed A Lb CP reqmt Equation describing CP Diet must supply 0.8 lb of CP so (A x 0.10) + (B x 0.35) = 0.8 lb CP Lb Feed B CP in Feed ACP in Feed B

6. Simultaneous Equations Lb TDN reqmt Equation describing TDN Diet must supply 4.0 lb of TDN so (A x 0.80) + (B x 0.50) = 4.0 lb TDN Lb Feed ALb Feed B TDN in Feed ATDN in Feed B

7. Simultaneous Equations 2 equations with the same unknowns 0.10A + 0.35B = 0.8 lb CP 0.80A + 0.50B = 4.0 lb TDN

8. Simultaneous Equations Multiply 1 equation by a factor that will make one unknown the same in both 0.10A + 0.35B = 0.8 lb CP 0.80A + 0.50B = 4.0 lb TDN 0.80/0.10 = 8, so multiply 1 st eq by 8

9. Simultaneous Equations 8 (0.10A + 0.35B) = 8 (0.8 lb CP) 0.8A + 2.8B = 6.4 lb new equation

10. Simultaneous Equations Subtract the 2 nd eq from new equation 0.8A + 2.8B = 6.4 lb new equation 0.8A + 0.5B = 4.0 lb 2 nd equation 0 + 2.3B = 2.4

11. Simultaneous Equations Solve for unknown 0 + 2.3B = 2.4 B = 2.4/2.3 B = 1.04 What was B? Lb Feed B

12. Simultaneous Equations Substitute 1.04 for B in either original eq 0.10A + 0.35B = 0.8 lb 0.10A + 0.35(1.04) = 0.8 0.10A = 0.8 – 0.364 0.10A = 0.436 A = 0.436/0.10 = 4.36 lb Feed A

13. Simultaneous Equations Our diet consists of: 1.04 lb Feed B 4.36 lb Feed A

14. Simultaneous Equations Check our work: 1.04 lb Feed B x 0.35 = 0.364 lb CP 4.36 lb Feed A x 0.10 = 0.436 lb CP 0.8 lb CP

15. Simultaneous Equations Check our work: 1.04 lb Feed B x 0.50 = 0.52 lb TDN 4.36 lb Feed A x 0.80 = 3.48 lb TDN 4.0 lb TDN