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Making a box

  1. Dec 4, 2007 #1
    1. The problem statement, all variables and given/known data
    We want to make an open box with squared base. Let x be the dimension of one side of the base and y the height of the box. We pay a cost of $1.00 /cm^2 for the base and $0.50/cm^2 for each side.
    The box must have a volume V = 6400 cm^3. Determine the dimensions x and y which will minimize the total cost of making the box.


    2. Relevant equations
    V = yx^2, TC = x^2 + 0.5xy


    3. The attempt at a solution
    I tried to solve the problem taking the partial derivatives with respect to x and y, which will give me the minimum values, but my results are not consistent. I am thinking on using Lagrange multipliers to solve the nonlinear minimization problem subject to the equality constraint of volume.
    Any suggestions?
    Thank you.
     
  2. jcsd
  3. Dec 4, 2007 #2

    Dick

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    Science Advisor
    Homework Helper

    In your TC function, remember that the box has four sides. Solve the volume constraint for, say, y. Then substitute that into TC. Now total cost is a function of only x. Minimize it. You certainly don't need lagrange multipliers.
     
  4. Dec 4, 2007 #3
    Thank you, I think this works.
     
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