# Area to cost based on parimiter

• Apr 21st 2012, 06:54 PM
blondedude092
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.
• Apr 21st 2012, 07:47 PM
skeeter
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
• Apr 21st 2012, 07:47 PM
Prove It
Re: Area to cost based on parimiter
Quote:

Originally Posted by blondedude092
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 \displaystyle \begin{align*} 2500\,\textrm{ft}^2 \end{align*}

\displaystyle \displaystyle \begin{align*} x\,h &= 2500 \\ h &= \frac{2500}{h} \end{align*}
• Apr 21st 2012, 08:04 PM
blondedude092
Re: Area to cost based on parimiter
So i am getting the equation of C = 100+10(x+(2500/x))

thanks!
• Apr 22nd 2012, 05:53 AM
Wilmer
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? • Apr 22nd 2012, 06:17 AM Prove It Re: Area to cost based on parimiter Quote: Originally Posted by Wilmer 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 \displaystyle \begin{align*} C = \frac{10x^2 + 100x + 25\,000}{x} \end{align*}
• Apr 22nd 2012, 06:31 AM
HallsofIvy
Re: Area to cost based on parimiter
Quote:

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

\displaystyle \displaystyle \begin{align*} x\,h &= 2500 \\ h &= \frac{2500}{h} \end{align*}

Typo. You mean, of course,
\displaystyle \displaystyle \begin{align*} x\,h &= 2500 \\ h &= \frac{2500}{x} \end{align*}
or
\displaystyle \displaystyle \begin{align*} x\,h &= 2500 \\ x &= \frac{2500}{h} \end{align*}
• Apr 22nd 2012, 06:51 AM
Prove It
Re: Area to cost based on parimiter
Quote:

Originally Posted by HallsofIvy
Typo. You mean, of course,
\displaystyle \displaystyle \begin{align*} x\,h &= 2500 \\ h &= \frac{2500}{x} \end{align*}
or
\displaystyle \displaystyle \begin{align*} x\,h &= 2500 \\ x &= \frac{2500}{h} \end{align*}

Of course, I meant h in terms of x :)