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Maximum value problem

  1. Jun 4, 2010 #1
    1. The problem statement, all variables and given/known data
    find the largest volume of a rectangular box that satisfies the following condition
    the sum of the height and horizontal perimeter does not exceed L
    2. Relevant equations
    critical point formula:
    system of equations must satisfy the following at critical values of x & y
    fx = 0
    fy = 0
    3. The attempt at a solution
    height + (width * depth) = L
    height*width*depth = V

    I do know the answer to be L^3/108 cubic units, but as to how to get that is beyond me.
  2. jcsd
  3. Jun 4, 2010 #2


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    Homework Helper

    Horizontal perimeter = 2(x+y) where x is the width and y is the depth.

    Area of the base is maximum when x = y. To have maximum volume, change h so that ( h + 2x + 2y) = L.

    If you put x = y, Volume V = h*x^2

    Put x = (L-h)/4. Find dV/dh and equate it to zero. Find h in terms of L and find V.
  4. Jun 5, 2010 #3
    ahh i got it now, thanks a bunch!
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