calculus?

posted by .

Hello can u help? I need a solution to calculus problem I have $500.00 to spend on fencing for a garden. The fence for the street side costs $30.00 per foot and the other three sides cost $10.00 per foot. what dimensions will give you a rectangle for the largest possible area?
How do you know it is for max area?

  • calculus? -

    with street side length x, and yard width y, then the cost is

    c = 30x + 10(x+2y)
    c=500, so

    500 = 40x + 20y, so
    y = 25 - 2x

    the area is given by

    a = xy = x(25-2x) = 25x - 2x^2
    da/dx = 25-4x

    da/dx=0 when x = 6.25. So, the yard is

    6.25 x 12.5

    The area has a max or min where da/dx = 0. Since a(x) is a parabola opening downward, it is a max.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. CALCULUS

    gardner wishes to encloe a rectangular 3000 square feet area with bushes on three sides and a fence on the 4th side .If the bushes cost $25.00per foot and the fence costs $10.00 per foot, find the dimensions that minimize the total …
  2. Business Calculus

    A rectangular garden of area 480 square feet is to be surrounded on three sides bya brick wall costing $12 per foot and on one side by a fence costing $5 per foot. Find the dimensions of the garden such that the cost of the materials …
  3. Calculus

    ABC Daycare wants to build a fence to enclose a rectangular playground. The area of the playground is 900 square feet. The fence along three of the sides costs $5 per foot and the fence along the fourth side, which will be made of …
  4. fdr

    a rectangular fence is constructed that will enclose 100 ft sq of land. three sides will be built from fencing that costs 10 dollars per foot and the 4th side will be built from fencing that costs 23 dollars per foot. find the dimensions …
  5. calculus

    A rectangular fence has to be built from both wood and metal so that opposite parallel sides of the fence are made from the same type of material. The wood costs $10 per foot and the metal costs $20 per foot of the fence used. If you …
  6. College Algebra

    A rectangular garden next to a building is to be fenced on three sides. Fencing for the side parallel to the building costs $60 per foot, and material for the other two sides costs $20 per foot. If $1,500 is to be spent on fencing, …
  7. Math

    My friend has $80 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $8/foot on one side, and cheaper metal fencing which costs $2/foot for the other three sides. What are the dimensions of the …
  8. MATH

    You would like to construct a 400-square-foot rectangular garden along your driveway. The fencing on the driveway side costs $15 per linear foot, while the fencing for the other three sides costs $8 per linear foot. Write an expression …
  9. Business Calculus

    Bill wants to fence in his rectangular garden so his precious produce will be protected. Three sides of the fence will be constructed with wire at $2 per linear foot and the fourth side will be constructed of wood fencing at a cost …
  10. Math

    I want to fence in a square vegetable patch. The fencing for the east and west sides costs $5 per foot, and the fencing for the north and south sides costs only $4 per foot. Find the total cost of the fencing as a function of the length …

More Similar Questions