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Constrained Minimization Problem(HELP )

  1. Mar 14, 2009 #1
    1. The problem statement, all variables and given/known data
    A closed rectangular box is made with two kinds of materials. The top and bottom are made with heavy-duty cardboard costing $0.36 per square foot, and the sides are made with lightweight cardboard costing $0.06 per square foot. Given that the box is to have a capacity of 162 cubic feet, what should its dimensions be if the cost is to be minimized?

    2. Relevant equations
    Surface Area A=2xy+2xz+2yz
    Volume= V=xyz=162

    partial derivitations are required to do this(which i know how to do)

    3. The attempt at a solution
    The hard part that I am trying to figure out is creating the Cost equation. All I need to know is what that equation would be and I can take care of everything afterwards. Like mentioned before in (2), the surface area A=2xy+2xz+2yz, but I have no idea how im going to create a cost function including the prices mentioned in the problem. PLEASE HELP. BLESS ANYONE WHO DOES. THANK YOU SO MUCH IN ADVANCE!!!
  2. jcsd
  3. Mar 14, 2009 #2


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    Hi MathNoob123! :wink:

    Multiply the area of heavy-duty cardboard by the cost per area, and multiply the area of lightweigh cardboard by the cost per area, and add :smile:
  4. Mar 14, 2009 #3

    I have already solved the problem, but thank you very much for replying. Really appreciate it.
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