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Math Help - Area to cost based on parimiter

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    Exclamation Area to cost based on parimiter

    I have an area A = 2500ft2 of a rectangular fence
    the area is found base * height
    the base is X and height is H

    Each fence post is $25; meaning $100 for all 4 of them
    Only 3 of the sides are being fenced, X X and H
    it costs $5 per ft on sides of X and $10 on H
    C = cost
    I am lost as to how to make a formula to tie all this information together. To make a formula in terms of C(x)=

    H is something i made up to hold the place of Height the rest are given.
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    Re: Area to cost based on parimiter

    cost ...

    C = 100 + 5x + 5x + 10h = 10x + 10h = 10(x+h)

    xh = 2500

    solve for h in the second equation, substitute the result in for h in the second equation to get the cost as a function of x
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    Re: Area to cost based on parimiter

    Quote Originally Posted by blondedude092 View Post
    I have an area A = 2500ft2 of a rectangular fence
    the area is found base * height
    the base is X and height is H

    Each fence post is $25; meaning $100 for all 4 of them
    Only 3 of the sides are being fenced, X X and H
    it costs $5 per ft on sides of X and $10 on H
    C = cost
    I am lost as to how to make a formula to tie all this information together. To make a formula in terms of C(x)=

    H is something i made up to hold the place of Height the rest are given.
    You can get it all in terms of x using the fact that the area is \displaystyle \begin{align*} 2500\,\textrm{ft}^2 \end{align*}

    \displaystyle \begin{align*} x\,h &= 2500 \\ h &= \frac{2500}{h} \end{align*}
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    Re: Area to cost based on parimiter

    So i am getting the equation of C = 100+10(x+(2500/x))

    thanks!
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    Re: Area to cost based on parimiter

    Right. Better to show this way: C = 100 + 10(x^2 + 2500) / x

    Cheapest when x = h : $1100 ; do you understand why?
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    Re: Area to cost based on parimiter

    Quote Originally Posted by Wilmer View Post
    Right. Better to show this way: C = 100 + 10(x^2 + 2500) / x

    Cheapest when x = h : $1100 ; do you understand why?
    Or even \displaystyle \begin{align*} C = \frac{10x^2 + 100x + 25\,000}{x} \end{align*}
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    Re: Area to cost based on parimiter

    Quote Originally Posted by Prove It View Post
    You can get it all in terms of x using the fact that the area is \displaystyle \begin{align*} 2500\,\textrm{ft}^2 \end{align*}

    \displaystyle \begin{align*} x\,h &= 2500 \\ h &= \frac{2500}{h} \end{align*}
    Typo. You mean, of course,
    \displaystyle \begin{align*} x\,h &= 2500 \\ h &= \frac{2500}{x} \end{align*}
    or
    \displaystyle \begin{align*} x\,h &= 2500 \\ x &= \frac{2500}{h} \end{align*}
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    Re: Area to cost based on parimiter

    Quote Originally Posted by HallsofIvy View Post
    Typo. You mean, of course,
    \displaystyle \begin{align*} x\,h &= 2500 \\ h &= \frac{2500}{x} \end{align*}
    or
    \displaystyle \begin{align*} x\,h &= 2500 \\ x &= \frac{2500}{h} \end{align*}
    Of course, I meant h in terms of x
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