Calculus

posted by .

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?

  • Calculus -

    Let x and y be the two side lengths of the full rectangle. The length x will be divided in two. The total lengths of fence needed will be

    L = 2x + 3y.

    You know that x y = 5,189,400 ft^2

    dL/dx = d/dx (2x + 3*5,189,400/x)
    = 2 - 15,568,200/x^2 = 0 at minimum L
    x^2 = 7,784,100
    x = 2790 ft y = 1860
    Quantity of fence needed = 2x + 3y = ?

Respond to this Question

First Name
School Subject
Your Answer

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 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?
  3. 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?
  4. 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 …
  5. Calculus

    A rancher wants to make an animal pen by fencing in an area of 2500000 square feet in a rectangular field and then divide it up with 5 fences down the middle parallel to one side. The rancher wants to use the shortest total length …
  6. 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 …
  7. area and perimeter

    a farmer wishes to build a fence around a rectangular field and divide it into two equal parts as well.the dividing fence must be parallel to one of the side of the field. you are asked to find dimension of the field of maximum area …
  8. calculas

    A landowner wants to fence in a rectangular area of 60000 square metres and divide it into three parts with two parallel fences both parallel to one side of the rectangle. Each part will have a different grazing crop for the herds. …
  9. 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?
  10. Calculus 1 optimization

    A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be …

More Similar Questions