Results 1 to 2 of 2

Math Help - help with lagrange in economics

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    3

    help with lagrange in economics

    I have a profit function = -100 + 80a - 0.1a^2 + 100b - 0.2b^2

    the question states relationg to the output of two products if total production (a + b = 500) find the solution that will maximize profit. solve the lagrange multiplier also.


    so i have reworked the formula to show = -100 + 80a - 0.1a^2 + 100b - 0.2b^2 - λ(500 - a - b)
    fa = 80 -0.2a - λ
    fb = 100 -0.4b - λ
    fλ = -500 + a + b

    i know i have to set fa, fb and fλ to 0 to solve the maximization point so im just not sure how to go from here using substitution to solve each p.derivative.

    if someone could help would be great
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jun 2008
    Posts
    7
    Hello

    You have the function:

    f(a,b,\lambda)=-100+80a-0.1a^2+100b-0.2b^2-\lambda(500-a-b)

    then, consider the equations:

    0=\dfrac{\partial f}{\partial a}=80-0.2a+\lambda

    0=\dfrac{\partial f}{\partial a}=100-0.4b+\lambda

     0=\dfrac{\partial f}{\partial a}=a+b-500

    From the first and second relation:

     a=400+5\lambda
     b=250+\dfrac{5\lambda}{2}

    And substiting in the last one:

     400+5\lambda+250+\dfrac{5\lambda}{2}=500

    Now, I suppose that you can conitnue...

    Best regards.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Economics Help
    Posted in the Business Math Forum
    Replies: 0
    Last Post: October 25th 2010, 11:54 AM
  2. Economics
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: June 14th 2009, 04:29 PM
  3. economics
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: May 14th 2009, 08:33 PM
  4. economics
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: May 14th 2009, 07:05 AM
  5. Economics
    Posted in the Business Math Forum
    Replies: 1
    Last Post: May 1st 2008, 12:09 AM

Search Tags


/mathhelpforum @mathhelpforum