Math

posted by .

A farmer plans to enclose a rectangular pasture adjacent to a river. (see figure). The pasture must contain 320,000 square meters in order to provide enough grass for the herd. What dimensions will require the least amount of fencing if no fencing is needed along the river?
x = m
y = m


Plz help...thnks

  • calulus - minimum -

    Since length x width = area
    we have length=area/width

    Let
    w=width of the pasture, and
    320000/w=length (parallel to river) of pasture
    Total length of fencing
    F=twice width + length
    =2w + 320000/w

    Find derivative of F with respect to w and equate to zero to find w.
    i.e.
    Solve for w in
    dF/dw=0

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus...again

    I'm gonna have abunch of questions, cause I have a test. >_< If you planened to fence a rectangular pasture that must contain 4000 sq meters, what dimensions would require the least amount of fencing?
  2. Applied Math- Gr.11

    A farmer wants to enclose three sides of a rectangular pasture unsing 1000 yards of fencing. The fourth side does not require fencing because it borders a river. What dimensions (length and width) should the farmer choose in order …
  3. Math

    Larry has 36 sections of wooden fencing. Each section is 6 feet long. He plans on using all the sections to surround a rectangular pasture. What is the area of the largest pasture he could create. How many different size rectangular …
  4. College Algebra

    A farmer has 100 yeards of fencing with which to enclose two adjacent rectangular pens both bordering a river. The farmer does not need to fence the side with the river. What should the dimensions of the two pens together (a rectangle) …
  5. Algebra - Math

    A farmer has 100 yards of fencing with which to enclose two adjacent rectangular pens - both bordering a river. The farmer does not need to fence the side with the river. What should the dimensions of the two pens Together (rectangle …
  6. Math

    A farmer needs to enclose three sides of a pasture with a fence (the fourth side is a river). The farmer has 42 meters of fence and wants the pasture to have an area of 220 sq-meters. What should the dimensions of the pasture be?
  7. Math

    farmer wants to enclose his pasture which is bordered by a river. If he uses 750 feet of fencing on three sides of the field, what is the largest area he can enclose?
  8. word problem

    a farmer has 800 yards of fencing to enclose a rectangular pasture. Since one side of the pasture boarders a river that side does not need to be fenced. if the side perpendicular to the river must be twice as long as the side parallel …
  9. Algebra 1

    Mr.Rush owns a dairy farm that is bordered on one side by a river.He wants to enclose a rectangular pastor that is bordered on one side by the river and on the other three sides by a 500 feet of fencing and a four foot gate.What must …
  10. Calc

    A rectangular page is to contain 30 sqaure inches of print. The margins on each side are 1 inch. Find the dimensions of the page sucha that the least amount of paper is used. A farmer plans to fence a rectangular pasture adjacent to …

More Similar Questions