anonymous
  • anonymous
A box with a square base and no top must have a volume of 10 000 cm3. If the smallest dimension is 5 cm, determine the dimensions of the box that minimize the amount of material used.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
By the way this is an optimization problem.
anonymous
  • anonymous
You need the formula for surface area here. That is S=x^2 + 4xy, so the formula for the volume of this box is (x^2)y=10,000 cm3. Solve for y and you get y=(10000/(x^2)). You can plug this into the original SA equation, so it has a single variable, then set the derivative equal to zero. Plug the number you get into the second derivative and if it is a negative number, than it is a max and if it is positive, then it is a min.
anonymous
  • anonymous
whoa

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anonymous
  • anonymous
@lord id listen to the Brain
anonymous
  • anonymous
Thank you =)
anonymous
  • anonymous
I did that. I got an answer. It seems to be wrong. And, that way we don't use the information: "Smallest dimension is 5"
anonymous
  • anonymous
I worked out the problem and I got 27.1442 as the minimum. I plugged it into the second derivative and got a positive answer, so it must be a min. as oppose to a max. You may have taken the wrong derivative.
anonymous
  • anonymous
The first derivative I had was: \[2x - 40000/x^{2} =0\] The second derivative was: \[2 + 40000/x^{3}=0\]
anonymous
  • anonymous
Thank you. That seems to be right.

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