A rancher plans to enclose a rectangular area of 2000 sq ft

[SigmaSweety19]

A rancher plans to enclose a rectangular area of 2000 square feet. To do this, he plans on using his barn to form one side of the barrier, using fencing for the other three sides. Due to wind conditons, the side parallel to the barn needs fencing that costs 45 per foot, while on the other two sides he can use fencing that costs $2 per foot. Find the dmensions of fencing the rancher should buy to minimize the total cost.

I have no idea how to set this up. Can someone please help me?????

 

[stapel]

A good way to start would be to do the same things you did back in algebra:

* Draw the picture.
* Pick variables and label the sides.
* Create a "length" equation for the fence, plugging in the variables and the known total fencing length.
* Solve the "length" equation for one of the variables.
* Create a "cost" equation for the fence, plugging in the variables and the known per-foot costs.
* Substitute for the one variable with what you got by solving the "length" equation.

Then move on to calculus by differentiating your "cost" equation.

If you get stuck, please reply showing (or describing) how far you have gotten, starting with your variables and how you defined them. Thank you.

Eliz.

 

[galactus]

As in the diagram I made, x=$2 per foot and y=$45 per foot.

Now, \(\displaystyle A=xy=2000\)

Cost = \(\displaystyle (2)2x+(45)y\)

\(\displaystyle \frac{dC}{dx}=4-\frac{90000}{x^{2}}\)

Set to 0 and solve for x.