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LordHades

  • 4 years ago

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.

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  1. LordHades
    • 4 years ago
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    By the way this is an optimization problem.

  2. brainshot3
    • 4 years ago
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    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.

  3. aminah.love18
    • 4 years ago
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    whoa

  4. aminah.love18
    • 4 years ago
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    @lord id listen to the Brain

  5. brainshot3
    • 4 years ago
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    Thank you =)

  6. LordHades
    • 4 years ago
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    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"

  7. brainshot3
    • 4 years ago
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    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.

  8. brainshot3
    • 4 years ago
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    The first derivative I had was: \[2x - 40000/x^{2} =0\] The second derivative was: \[2 + 40000/x^{3}=0\]

  9. LordHades
    • 4 years ago
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    Thank you. That seems to be right.

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