Thread: 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.

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

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

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

thanks!

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

Cheapest when x = h : $1100 ; do you understand why?

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

Originally Posted by Prove It

You can get it all in terms of x using the fact that the area is

Typo. You mean, of course,

or

Originally Posted by HallsofIvy

Typo. You mean, of course,

or

Of course, I meant h in terms of x