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Finding the dimensions of a rectangular box

  1. Feb 15, 2012 #1
    I'm worried about the process of solving this problem, can anyone help me?

    We are to make a rectangular box, including the top, that has a volume of 144 cubic inches and for which the base is twice as wide as it is deep. The bottom, which must be strong, is made of a material that is three times as expensive as that used for the sides and the top. Find the dimensions of the box that minimize its cost.

    I know I must have two equations with two variables in total but I'm not sure what to do after that. Maybe 144=(2x)(x)(y)? and another

    Thanks to anyone who can shed some light on this for me, I've been trying for a bit but not sure where to start.
  2. jcsd
  3. Feb 15, 2012 #2


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    You wrote down an equation for the volume of the box. If you want to minimize the cost, you also need an equation for the cost. That will depend on the amount of material you need, in other words the surface area of the box.
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