Calculus

A rectangular field is to be enclosed by a fence and divided into three lots by fences parallel to one of the sides. Find the dimensions of the largest field that can be enclosed with 800 feet of fencing.

Help me please!!!!!!!!!!! THANK YOU

  1. 👍
  2. 👎
  3. 👁
  1. 2 * L + 4*w = 800
    so
    L = 400 - 2w

    A = L * w
    A = (400 -2w)w
    A = -2 w^2 +400 w
    dA/dw = 0 at max
    = -2 w + 200
    w = 100
    L = 400 -200 = 200

    1. 👍
    2. 👎
  2. thanks

    1. 👍
    2. 👎
  3. hmmm

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    A farmer wants to fence in an area of 15000 m² in a rectangular field and then divide it into half with a fence parallel to one sides of the rectangle. How can he do this so as to minimize the cost of the fence?

  2. 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

  3. Calc.

    Please help solve this, A farmer has 600m of fence and wants to enclose a rectangular field beside a river. Determine the dimensions of the fence field in which the maximum area is enclosed. (Fencing s required on only three

  4. calculus

    Sam has 1200 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. Express the area of the field as a function of its dimension. Find the dimensions of the

  1. calculus (optimization)

    a rectangular study area is to be enclosed by a fence and divided into two equal parts, with the fence running along the division parallel to one of the sides. if the total area is 384 square feet, find the dimensions of the study

  2. Math

    A rancher wants to fence in an area of 2000000 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

    OPTIMIZATION PROBLEM: "A rectangular field is to be enclosed on four sides with a fence. Fencing costs $7 per foot for two opposite sides, and $5 per foot for the other two sides. Find the dimensions of the field of area 620ft^2

  4. math

    A rectangular field is to be enclosed on four sides with a fence. Fencing costs $8 per foot for two opposite sides, and $2 per foot for the other sides. Find the dimensions of the field of area 900 ft2 that would be the cheapest

  1. precalculus

    A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He does not need a fence along the river (see the figure). What are the dimensions of the field of largest area that he can

  2. 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?

  3. Precalculus

    A farmer with 10000 meters of fencing wants to enclose a rectangular field and divide it into two plots with a fence parallel to the sides. What is the largest area that can be enclosed?

  4. Algebra

    A total of 800 m of fencing material is used to enclose a rectangular field and to divide the field into four portions by fences parallel to one of the sides of the field. Find the maximum area which can be enclosed in this

You can view more similar questions or ask a new question.