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Math Help - Major Calculus HELP

  1. #1
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    Major Calculus HELP

    well i'm been stuck on this question for the longest time in the world... can someone help me please?
    Q:
    Gym Sock Compant manufactures cotton athletic socks. Production is partially automated through the use of robots. Daily operating cost amount to $50 per labourer and $30 per robot.

    The number of pairs of socks the company can manufacture in a day is given by x=50(n^0.6) (r^0.4) (A Cobb Douglas production formula), where x is the number of pairs of socks that cn be manufactured by N labourers and R robots.

    Assuming that the compant wishes to produce 1000 pairs of socks per day at a minimom cost, how many labourers and how many robots should it use? You will need to formulate a cost function. Express your cost function as a function of robots, r, and continue from there.

    Your answers for robots and labohrers will turn out to be fractional numbers. But you do not want fractional number of people or robots, naturally, so you will need to round your answers to interger values for r and n. Choose the most economical integer values, yet still satisfying the requirement of producing at least 1000 pairs of socks.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Major Calculus HELP

    We have the objective cost function:

    C(n,r)=50n+30r

    subject to the constraint:

    g(n,r)=n^{\frac{3}{5}}r^{\frac{2}{5}}-20=0

    Using Lagrange multipliers, we find:

    50=\lambda\frac{3}{5}\left(\frac{r}{n} \right)^{\frac{2}{5}}

    30=\lambda\frac{2}{5}\left(\frac{n}{r} \right)^{\frac{3}{5}}

    From this system, what relationship between n and r can we find?
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  3. #3
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    Re: Major Calculus HELP

    is there another method besides using Lagrange multipliers cause i haven't learned that in school yet
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  4. #4
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    Re: Major Calculus HELP

    the exact same problem posted earlier ... by someone else?

    Calculus - Cost & Production applied problems
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