math

An ostrich farmer wants to enclose a rectangular area and then divide it into 4 pens with fencing parallel to one side of the rectangle. There are 720 feet of fencing available to complete the job. What is the largest possible total area of the 4 pens?

  1. 👍
  2. 👎
  3. 👁
  1. let the width of one of the pens be x, let its length be y

    so we have 8x + 5y = 720
    y = (720 - 8x)/5 = 144 - 8x/5

    area = 4xy
    = 4x(144 - 8x/5)
    = 576x - (32/5)x^2

    d(area)/dx = 576 - 64x/5
    = 0 for a max of area
    64x/5 = 576
    64x = 2880
    x = 45

    largest total area = 4(45)(144 - 8(45)/5)
    = 12960 ft^2

    check my arithmetic

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    A farmer has 1500 feet of fencing in his barn. He wishes to enclose a rectangular pen. Subdivided into two regions by a section of fence down the middle, parallel to one side of the rectangle. Express the area enclosed by the pen

  2. 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?

  3. Math

    a farmer wants to put a fence around a rectangular field and then divide the field into three rectangular plots by placing two fences parallel to one of the sides. if the farmer can only afford 1000 yards of fencing, what

  4. Math

    1. A gardener has 140 feet of fencing to fence in a rectangular vegetable garden. Find the dimensions of the largest area he can fence. Find the possible rectangular area he can enclose. 2. Suppose a farmer has a large piece of

  1. 12th grade

    A farmer has 100 yards of fencing to form two identical rectangular pens and a third pen that is twice as long as the other two pens, as shown in the diagram to the right. All three pens have the same width, x. Which value of y

  2. Algebra

    Farmer Ed has 9,000 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, what is the largest area that can be​ enclosed?

  3. Calculus 1

    If you have 280 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?

  4. Calculus BC

    A farmer has 100 yards of fencing to form two identical rectangular pens and a third pen that is twice as long at the other two pens, as shown in the diagram at right. All three pens have the same width, x. What value of y

  1. math

    A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed?

  2. Calculus

    A farmer has 600 meters of fencing and wishes to enclose a rectangular field and then divide it into 3 separate plots. Set up an equation for the total length of fencing in terms of lengths x and y. Set up an eqaution for the

  3. Pre-Calc

    How do you do this? A farmer has 336 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area.

  4. Math

    Eighty metres of fencing are available to enclose a rectangular area. What are the dimensions that enclose the max area. What is max area?

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