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Optimization box with maximum volume?

  1. Jun 18, 2012 #1
    1. The problem statement, all variables and given/known data
    A manufacturer wants to design a box having a square base and a surface area of 108m^2. What dimension will produce a box with maximum volume?


    2. Relevant equations
    a=x^2+4xy
    V=x^2y
    a=108m^2
    3. The attempt at a solution
     
    Last edited: Jun 18, 2012
  2. jcsd
  3. Jun 18, 2012 #2
    You can use the constraint given for the area to solve either y as a function of x or vice versa. Then you can find the maximum for V(x, y(x)) or V(x(y), y).
     
  4. Jun 18, 2012 #3
  5. Jun 18, 2012 #4

    Ray Vickson

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    Science Advisor
    Homework Helper

    Is the box open or closed? That affects the surface area.

    RGV
     
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