Post a New Question

Calculus

posted by .

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 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?

You answered:

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

Now I have a stupid question... what happened to the y in the c= equations?

  • Calculus -

    x y = 1
    so
    y = 1/x

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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?
  2. math

    A farmer plans to enclose a rectangular region, using part of his barn for one side and fencing for the other three sides. If the side parallel to the barn is to be twice the length of an adjacent side, and the area of the region is …
  3. 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 …
  4. calculus

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

    A retail lumberyard plans to store lumber in a rectangular region adjoining the sales office. The region will be fenced on three sides and the fourth side will be bounded by the wall of the office. Find the dimensions of the region …
  6. Math

    A farmer uses 1034 meters of fencing to enclose a rectangular region and also to subdivide the region into three smaller rectangular regions by placing a fence parallel to one of the sides. Find the demensions that produce the greatest …
  7. 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 …
  8. math

    A rancher wishes to use 86 ft of fencing to enclose a rectangular paddock and subdivide the region into three smaller areas. If the total enclosed area is 225 ft2, find the dimensions of the enclosed region.
  9. math

    A rancher wishes to use 86 ft of fencing to enclose a rectangular paddock and subdivide the region into three smaller areas. If the total enclosed area is 225 ft2, find the dimensions of the enclosed region.
  10. Math

    A man owns a rectangular piece of land. The land is divided into four rectangular pieces, known as Region A, Region B, Region C, and Region D. One day his daughter, Nancy, asked him, what is the area of our land?

More Similar Questions

Post a New Question