Wednesday

October 1, 2014

October 1, 2014

Posted by **Chris** on Friday, December 16, 2011 at 5:54am.

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 -
**drwls**, Friday, December 16, 2011 at 6:13amThis question has already been answered by Damon

- calculus -
**Chris**, Friday, December 16, 2011 at 6:16amYes, I know, but I i had question about the answer... I'm math stupid :)

- calculus -
**Damon**, Friday, December 16, 2011 at 8:37amThe smaller of x or y will be the expensive fence along the road.

**Answer this Question**

**Related Questions**

Calculus - Damon, Help :) A rancher plans to set aside a rectangular region of ...

Calculus - A rancher plans to set aside a rectangular region of one square ...

Calculus - A rancher wants to fence in an area of 500000 square feet in a ...

Calculus - A rancher wants to fence in an area of 5189400 square feet in a ...

Calculus-Applied Optimization Quiz Problem - A rancher wants to fence in a ...

Calc - A rancher wants to fence in an area of 1500000 square feet in a ...

CALC - A rancher wants to fence in an area of 1500000 square feet in a ...

Calculus - A rancher wants to make an animal pen by fencing in an area of ...

math - I've tried this many times, but I keep getting a really big answer. A ...

math - a landscape architect plans to enclose a 3000 square foot rectangular ...