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Math Help - Tough Optimization Question

  1. #1
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    Tough Optimization Question

    Can someone send me the full steps so i can learn from it, i missed the lecture today so i didn't get the step by step walk through of the solution i'm having such a hard time with the optimization unit it's really tough... and our textbooks only give us to answer so i have no idea how to solve the question.

    it's #6
    http://smcewen.pbworks.com/f/Sec3_3+Extra+Practice.pdf
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  2. #2
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    Re: Tough Optimization Question

    Your restriction is the the volume must be 240
    The volume in each box is given by x^2y so x^2y=240

    The area of wire that is needed is 2(x)(2x)+2(x)(y)+(2x)(y)=4x^2+4xy the sum of the surface areas
    Let A=4x^2+4xy

    You want to minimise A so first get A in terms of only x, then find when \frac{dA}{dx} equals zero, confirm that it is a minimum for the area not a maximum. You will probably get 2 answers, remember than you are restricted in how big/small x can be.
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