Simultaneous Equations Diet Balancing Simultaneous Equations Used to

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 • Feed A – 10% CP, 80% TDN • Feed B – 35% CP, 50% TDN

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

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

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

Simultaneous Equations • 2 equations with the same unknowns • 0. 10 A + 0. 35 B = 0. 8 lb CP • 0. 80 A + 0. 50 B = 4. 0 lb TDN

Simultaneous Equations • Multiply 1 equation by a factor that will make one unknown the same in both • 0. 10 A + 0. 35 B = 0. 8 lb CP • 0. 80 A + 0. 50 B = 4. 0 lb TDN • 0. 80/0. 10 = 8, so multiply 1 st eq by 8

Simultaneous Equations • 8 (0. 10 A + 0. 35 B) = 8 (0. 8 lb CP) • 0. 8 A + 2. 8 B = 6. 4 lb new equation

Simultaneous Equations • Subtract the 2 nd eq from new equation • 0. 8 A + 2. 8 B = 6. 4 lb new equation • 0. 8 A + 0. 5 B = 4. 0 lb 2 nd equation • 0 + 2. 3 B = 2. 4

Simultaneous Equations • Solve for unknown • 0 + 2. 3 B = 2. 4 • B = 2. 4/2. 3 • B = 1. 04 • What was B? • Lb Feed B

Simultaneous Equations • Substitute 1. 04 for B in either original eq • 0. 10 A + 0. 35 B = 0. 8 lb • 0. 10 A + 0. 35(1. 04) = 0. 8 • 0. 10 A = 0. 8 – 0. 364 • 0. 10 A = 0. 436 • A = 0. 436/0. 10 = 4. 36 lb Feed A

Simultaneous Equations • Our diet consists of: • 1. 04 lb Feed B • 4. 36 lb Feed A

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

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