Lagrange Multiplier

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  1. marcell_'s Avatar
    • Junior Member
    Lagrange Multiplier
    Could anyone work through this example for me?

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    Much appreciated
  2. Groat's Avatar
    • PS Helper
    • TSR Idol
    Re: Lagrange Multiplier
    (Original post by marcell_)
    x
    Okay, so the first step is to formulate your constraint. From the information given, can you form one?
  3. marcell_'s Avatar
    • Junior Member
    Re: Lagrange Multiplier
    (Original post by Groat)
    Okay, so the first step is to formulate your constraint. From the information given, can you form one?
    g2 (x,y) = x + y – 300 = 0

    Would that be correct?
  4. Groat's Avatar
    • PS Helper
    • TSR Idol
    Re: Lagrange Multiplier
    Sticking with the notation:

     Q_1 + Q_2 \le 300
  5. ryanboi's Avatar
    • Exalted and Worshipped Member
    • Posts: 1,064
    Re: Lagrange Multiplier
    (Original post by marcell_)
    Could anyone work through this example for me?

    Spoiler:
    Show


    Much appreciated
    Do you have the answer to the question? Because I am trying to work it out but I am not sure if I have done it correctly. Thanks
  6. marcell_'s Avatar
    • Junior Member
    Re: Lagrange Multiplier
    (Original post by Groat)
    Sticking with the notation:

     Q_1 + Q_2 \le 300
    P_1Q_1 + P_2Q_2 -(20000 + 100(Q_1+Q_2))

subject to Q_1 + Q_2 \le 300?

    Sadly not Ryan.
  7. Groat's Avatar
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    Re: Lagrange Multiplier
    (Original post by marcell_)
    P_1Q_1 + P_2Q_2 -(20000 + 100(Q_1+Q_2))

subject to Q_1 + Q_2 \le 300?

    Sadly not Ryan.
    Can you write the first function in terms of Q_1 and Q_2 only? Once you can, you can then apply the Lagrange technique.

    (Original post by ryanboi)
    Do you have the answer to the question? Because I am trying to work it out but I am not sure if I have done it correctly. Thanks
    Spoiler:
    Show


     Q_1 = 170
     Q_2 = 130
     Profit = 82250

    I'm pretty sure that's correct!

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