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Math Help - Total cost of box as a function of x?

  1. #1
    Newbie KeizerSoze's Avatar
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    Question [SOLVED] Total cost of box as a function of x?

    Hi,

    I just started taking a Pre-Calculus math course in College. I took this course years ago and since then have forgotten most of what I have learned. I have come across the following question which I am stuck on.

    A box with a square base has a volume of 600 cubic cm. If the material for the 4 sides and the top costs 5 cents per square cm and the material for the reinforced base costs 10 cents per square cm, express the total cost C of material (in cents) as a function of x, where x is the length of a side of the square base. Write the function in simplified form.

    I have gotten this far:

    600 = w^2*h
    h = 600/w^2

    Area = 2w^2 + 4*w(600/w^2)
    Area = 2w^2 + 2400/w


    The answer that is given to me is C(x) = 15x^2 + 12000/x

    I can see that if I multiply the 2400 by 5 I will get the 12000/x but I don't understand where the 15x^2 comes from.
    Last edited by KeizerSoze; September 25th 2011 at 09:57 PM.
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  2. #2
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    pickslides's Avatar
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    Re: Total cost of box as a function of x?

    You need to multiply the parts through by 5 or 10 depending on their worth.

    \displaystyle C(x) = 5\times \left( x^2+ \frac{2400}{x}\right)+10\times \left( x^2\right) = \dots
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  3. #3
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    Re: Total cost of box as a function of x?

    since the cost of top and base are different so you have to multiply top area with 5 and base area with 10 as
    C(x)=10x^2+5x^2+5(\frac{2400}{x})
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  4. #4
    Newbie KeizerSoze's Avatar
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    Re: Total cost of box as a function of x?

    Thank you very much guys! Now it is clear to me Most impressive how quickly that was answered!
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