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Applied maximum and minimum problems

  1. Oct 27, 2010 #1
    Q: A box will be built with a square base and an open top. Material for the base costs $8 per square foot, while material for the sides costs $2 per square foot. Find the dimensions of the box of maximum volume that can be built for $2400.







    x | 0 _ 10
    y | 300 0 20
    V | 0 0 2000

    Therefore x=10, y=20

    Chk [tex]D^{2}_{x}V<0:[/tex]
    [tex]D^{2}_{x}V=y+xD_{x}y-4x=y-(2+y/x)x-4x<0[/tex] when x=10, y=20
    => abs max
    Last edited: Oct 27, 2010
  2. jcsd
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