Transcript Powerpoint on 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
• 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
CP in Feed A
Lb CP reqmt
Lb Feed B
CP in Feed B
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 Feed A
Lb Feed B
TDN in Feed A
Lb TDN reqmt
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