Wednesday
October 1, 2014

Homework Help: calculus

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

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

Answer this Question

First Name:
School Subject:
Answer:

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 ...

Search
Members