Maximum Area-Calculus-Edit

posted by .

We have 900 ft of fencing and we want to construct a back yard. If we are using the building as part of the barrier for the yard what are the dimensions that allow maximum area?

I am not even sure how to start though I know I am supposed to calculate the derivative of the setup. Thank you

Here is the image. imgur F5NJVqp

  • Maximum Area-Calculus-Edit -

    perimeter = 2 W + L = 900
    so
    L = (900 - 2W)

    A = W L
    A = W (900 -2W)
    A = 900 W - 2 W^2
    now you can complete the square for the parabola and find the vertex or you can use calculus

    dA/dW = 0 for max = 900 - 4 W
    W = 225

    900 = 2 W + L
    900 = 450 + L
    L = 450

    glad you learned calculus and did not have to find the vertex of that parabola? :)

  • Maximum Area-Calculus-Edit -

    Oh, although I can not see your image I see your note on your earlier question answered by Steve.
    If only 100 feet of the building is used then
    2 W + L + (L-100) = 900
    2 W + 2 L - 100 = 900
    2 W + 2 L = 1000
    then continue as before

  • Maximum Area-Calculus-Edit -

    THANK YOU SO MUCH! I got 250 for each dimension :)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Chris wants to make an enclosed rectangular area for a mulch pile. She wants to make the enclosure in such a way as to use a corner of her back yard. She also wants it to be twice as long as it is wide. Since the yard is already fenced, …
  2. math

    Susan's back yard is rectangular with dimensions 39 yd. by 71 yd. Carlos's back yard is rectangular with dimensions 30 yd. by 50 yd. How much larger is the area of Susan's back yard than the area of Clarlos's back yard?
  3. Pre-Algebra-math

    Mr.jones bought 20 yards of fencing to make pen for dog pen will be in rectangle shape, the fencing comes in 1 yard section, wants the MAXIMUM areafor his dog to run, what dimension will give the pen the biggest space for dog to run?
  4. Maximum Area

    We have 900 ft of fencing and we want to construct a back yard. If we are using the building as part of the barrier for the yard what are the dimensions that allow maximum area?
  5. 5th grade math

    suppose you are building a fence for a garden in your yard. your yard is 50 ft wide and has an area of 500 square ft. your father has 88 feet of garden fencing,so your garden has to have a perimeter of 88 ft. how big an area would …
  6. calculus

    I got half of this problem wrong and I DO NOT know where and how to fix. I cannot use my calculator and have to show my work. Question: You have a 500 metre roll of fencing and a large field. You want to construct a rectangular playground …
  7. calculus help

    Farmer Brown wants to fence in a rectangular plot in a large field, using a straight rock wall that is already there as the north boundary. The fencing for the east and west sides of the plot will cost $3 a yard, but she needs to use …
  8. AP Calculus

    The management of a large store has 1600 feet of fencing to fence in a rectangular storage yard using the building as one side of the yard. If the fencing is used for the remaining 3 sides, find the area of the largest yard possible.
  9. Math, Quadratic Functions

    A rectangular chicken yard was built against an existing barn wall (as shown in the picture). 30 m of fencing was used to enclose the yard. a) Find the dimensions of the yard its area is 108 m! How to solve this problem..?
  10. Algebra

    Ian wants to fence three sides of a rectangular exercise yard for his dog. The fourth side of the exercise yard will be a side of the house. He has 100 feet of fencing available. Find the dimensions that will enclose the maximum area.

More Similar Questions