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anonymous

  • 5 years ago

LaGrange Multipliers Help Please!

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  1. anonymous
    • 5 years ago
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    f(x,y,z) = xy + 2xz + 2yz Constraint xyz = 32 I know the steps of finding the partial derivatives but I get stuck after that. Do I also need to find the Partial derivative of \[\lambda\] - Having 3 variables is proving difficult for me! Any help as to how I can solve it? Thanks!

  2. anonymous
    • 5 years ago
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    Step 1 Fx & Fy i.e differentiate with respect to x , Fx ,then differentiate with respect to y, Fy. Step 2 F x=0 and Fy=0 ( solve simultaneously ) Step 3 Substitute in the constraint to get the critical points (x,y,z). Solve for x in terms of \[\lambda\].

  3. anonymous
    • 5 years ago
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    What about the partial derivative with respect to z?

  4. anonymous
    • 5 years ago
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    there are two methods to working this? You can find it also and by finding the z

  5. anonymous
    • 5 years ago
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    This is my attempt, does not necessarily have to be correct. F( x,y,λ) = f(x,y)- λ[ g(x,y)- c] Fx= y+2z-λyz Fy= x+2z-λxz Fy=0 x+2z-λxz=0 λ= x+2z/xz Fx=0 y+2z-λyz=0 λ= y+2z/yz solve simultaneously

  6. anonymous
    • 5 years ago
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    Continue from here... Also Fλ= xyz, that why it is not necessary to find it because it give us the constraint, which already given.

  7. anonymous
    • 5 years ago
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    How do you solve simultaneously when we habe xz i the first eqn and yz in the second?

  8. anonymous
    • 5 years ago
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    but we have λ in both

  9. anonymous
    • 5 years ago
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    Yes, and...

  10. anonymous
    • 5 years ago
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    lol

  11. anonymous
    • 5 years ago
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    λ- (y+2z/yz)=0 equation 1 λ- (x+2z/xz)=0 equation 2

  12. anonymous
    • 5 years ago
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    or you could solve by letting λ= λ

  13. anonymous
    • 5 years ago
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    Disclaimer, this is how I would attempt this question based on how i was taught

  14. anonymous
    • 5 years ago
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    Haha! I'm only kidding!

  15. anonymous
    • 5 years ago
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    do u agree or not?

  16. anonymous
    • 5 years ago
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    I'll quickly give it a go and see what I get...

  17. anonymous
    • 5 years ago
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    well its not quiet... clear so I need to get help

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