simultaneous equations diet balancing. simultaneous equations used to balance for 2 nutrients...
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Simultaneous Equations Simultaneous Equations Diet BalancingDiet 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
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 BCP in Feed A CP in Feed B
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 A Lb Feed BTDN in Feed A TDN in Feed B
Simultaneous Equations• 2 equations with the same unknowns• 0.10A + 0.35B = 0.8 lb CP• 0.80A + 0.50B = 4.0 lb TDN
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
Simultaneous Equations• 8 (0.10A + 0.35B) = 8 (0.8 lb CP)• 0.8A + 2.8B = 6.4 lb new equation
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
Simultaneous Equations• Solve for unknown• 0 + 2.3B = 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• 0.10A + 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
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