1 / 15

Simultaneous Equations Diet Balancing

Simultaneous Equations Diet Balancing. 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. Simultaneous Equations. Identify feeds and their composition

kai-hunt
Download Presentation

Simultaneous Equations Diet Balancing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 • 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 CP reqmt Lb Feed A Lb Feed B CP in Feed A CP in Feed B

  6. Simultaneous Equations • 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 TDN reqmt Lb Feed A Lb Feed B TDN in Feed A TDN 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 1st 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 2nd eq from new equation • 0.8A + 2.8B = 6.4 lb new equation • 0.8A + 0.5B = 4.0 lb 2nd 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

More Related