# calculus

posted by .

Damon help again :) (last one I promise)
why is X along the road sqrt2/2?

] A rancher plans to set aside a rectangular region of one square kilometer for cattle and wishes to build a wooden fence to enclose the region. Since one side of the region will run along the road, the rancher decides to use a better quality wood for that side which costs three times as much as the wood for the other sides. What dimensions will minimize the cost of the fence?

x y = 1

c = 3 x + x + 2 y = 4 x + 2 y

c = 4 x + 2/x

dc/dx = 4 - 2/x^2
= 0 for minimum

4 = 2/x^2
x^2 = 1/2
x = 1/sqrt 2 = sqrt 2/2 along road
y = sqrt 2

• calculus -

This question has already been answered by Damon

• calculus -

Yes, I know, but I i had question about the answer... I'm math stupid :)

• calculus -

The smaller of x or y will be the expensive fence along the road.

## Similar Questions

1. ### math

I've tried this many times, but I keep getting a really big answer. A rancher wants to fence in an area of 2500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What …
2. ### Calculus

A rancher wants to fence in an area of 5189400 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
3. ### Calculus

A rancher wants to fence in an area of 500000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side. What is the shortest length of fence that the rancher can use?
4. ### CALC

A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
5. ### Calculus

A rancher plans to set aside a rectangular region of one square kilometer for cattle and wishes to build a wooden fence to enclose the region. Since one side of the region will run along the road, the rancher decides to use a better …
6. ### Calculus

Damon, Help :) A rancher plans to set aside a rectangular region of one square kilometer for cattle and wishes to build a wooden fence to enclose the region. Since one side of the region will run along the road, the rancher decides …
7. ### calculus

A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side. Length of fence:______ feet *obviously I'm bad at word problems but that's …
8. ### Calculus-Applied Optimization Quiz Problem

A rancher wants to fence in a rectangular area of 23000 square feet in a field and then divide the region in half with a fence down the middle parallel to one side. What is the smallest length of fencing that will be required to do …
9. ### Calculus

A rancher wants to build a rectangular fence next to a river, using 100 yd of fencing. What dimensions of the rectangle will maximize the area?
10. ### Calc

A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side. What is the shortest length of fence that the rancher can use?

More Similar Questions

Post a New Question