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Thread: Help with this word problem. Fining the minimum cost.

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    Help with this word problem. Fining the minimum cost.

    The question as written is

    You need to make a closed box with a square base and volume of 32,000 inches cubed . The material for the top and bottom of the box costs \$1 per square inch, and the materials for the sides cost \$0.25 per square inch, Find the dimensions of the box that minimize the cost.

    Okay so the problem I'm having here is setting up the equation. The volume of a cube is x^3. The area of a square is x^2. So I should set the price equal to the top and bottom as

    \$1(x2) + $1(x2) and I get 2x2. The price for the sides is \$0.25(x2)(4) which just comes to \$1(x2) too. So the cost function should just be 3x2 right? And the derivative is 6x. But if I set that 6x=0 I just get x=0 for the critical point. But that doesn't look right to me. Where did I mess up?
    Last edited by skeeter; Mar 15th 2017 at 01:23 PM.
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    Re: Help with this word problem. Fining the minimum cost.

    what makes you think it's a cube? (it may not be). The base is square, but that doesn't mean the height is the same length as the base length/width.

    $V = x^2h = 32000 \implies h = \dfrac{32000}{x^2}$

    $C = (1)x^2 + (1)x^2 + (0.25) \cdot 4xh = 2x^2 + \dfrac{32000}{x}$

    determine $\dfrac{dC}{dx}$ and minimize the cost ...
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    Re: Help with this word problem. Fining the minimum cost.

    ...thats a good point. I guess I assumed box=cube
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    Re: Help with this word problem. Fining the minimum cost.

    okay so for my critical points I got x=0, x=20. After doing the first derivative test I conclude that 20 is a local minimum thus $20 is the answer to to the second part. What is it asking me though when it tells me to find the "dimensions"? Is that just asking what you found with the V=x^2(h)?
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    Re: Help with this word problem. Fining the minimum cost.

    $x$ is in inches ...
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    Re: Help with this word problem. Fining the minimum cost.

    So then I just plug 20 into the cost function then?

    I get 2,400. If thats in cents I move the decimal place over twice and the cost is $24?
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    Re: Help with this word problem. Fining the minimum cost.

    <slaps forehead> ...

    the top alone is 20" by 20" = 400 square inches ... wasn't the cost one dollar per square inch for the top and bottom? What does that tell you?
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    Re: Help with this word problem. Fining the minimum cost.

    I don't know thats why i'm asking. If I could get a straight answer that'd be great. Despite what you may think I got an 83 on my last test and more than half my class has already dropped. I'm not stupid.

    so its $800 for the top and bottom and $1600 for the sides so is the total cost is $2400?
    Last edited by XxXScorpionXxX; Mar 15th 2017 at 04:10 PM.
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    Re: Help with this word problem. Fining the minimum cost.

    Good luck.
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    Re: Help with this word problem. Fining the minimum cost.

    I don't get it why even do this in your spare time if people who aren't savants at mathematics annoy you?
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    Re: Help with this word problem. Fining the minimum cost.

    I get annoyed when someone doesn't pay attention to the units clearly stated in the original problem statement. So, don't worry, this will be my final post to any of your threads.
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