math

posted by .

i am having serious optimization problems. i don't get it!!! plz help.

a 216-m^2 rectangular pea patch is to be enclosed by a fence and divided into two equal parts by another fence parallel to one of the sides. what dimensions for the outer rectangle will require the smallest total length of fence? how much fence will be needed?

you are designing a 1000-cm^3 right circular cylindrical can whose manufacture will take waste into account. tehre is no waste in cutting the aluminum for the side, but the top and bottom of radius r will be cut from squares that measure 2r units on a side. the total amount of aluminum used up by the can will therefore be
A = 8r^2 + 2(pi)rh
rather than the A = 2(pi)r^2 + 2(pi)rh in Example 4. In example 4 the ratio of h to r for the most economical can was 2 to 1. what is the ratio now?

  • math -

    Considering all rectangles with a given perimeter, the square encloses the greatest area.

    Proof: Consider a square of dimensions x by x, the area of which is x^2. Adjusting the dimensions by adding a to one side and subtracting a from the other side results in an area of (x + a)(x - a) = x^2 - a^2. Thus, however small the dimension "a" is, the area of the modified rectangle is always less than the square of area x^2.

    Considering all rectangles with a given perimeter, the square encloses the greatest area.
    Proof: Consider a square of dimensions x by x, the area of which is x^2. Adjusting the dimensions by adding a to one side and subtracting a from the other side results in an area of (x + a)(x - a) = x^2 - a^2. Thus, however small the dimension "a" is, the area of the modified rectangle is always less than the square of area x^2.

    Considering all rectangles with the same area, the square results in the smallest perimeter for a given area.


    Considering all rectangles with a given perimeter, one side being another straight boundry, the 3 sided
    rectangle enclosing the greatest area has a length to width ratio of 2:1

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. shortest fence

    this is my last question from applications of derivatives! A 216m^2 rectangular pea patch is to be enclosed by a fence and divided into two equal parts by another fence parallel to one of the sides. What dimensions for the outer rectangle …
  2. calculus

    A 384 square meter plot of land is to be enclosed by a fence and divided into equal parts by a fence parallel to one pair of sides. What dimensions of the outer rectangle will minimize the amount of force used?
  3. Math

    A rectangular study area is to be enclosed by a fence and divided into two equal parts, with a fence running along the division parallel to one of the sides. if the total area is 384 ft^2, find the dimensions of the study area that …
  4. algebra

    The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of …
  5. Grade 11 Math

    A rectangular dog run is to be enclosed by a fence and then divided into two smaller rectangular areas by a fence parallel to one of the sides. If 54m of fence is available, find the dimensions of the dog run of greatest possible area. …
  6. math

    the length of a rectangular field is 18 m longer than the width. the field is enclosed with fencing and divided into two parts with a fence parallel to the shoter sides. if 216 m of fencing are required to the shoter sides. if 216 …
  7. Calculus 1

    A rectangular field is enclosed by a fence and separated into two parts by a fence parallel to one of the sides. If 600 m of fencing is available, what should the dimensions be so that the area is a maximum?
  8. precalculus

    A rectangular field is to be enclosed by a fence and divided into three equal rectangular parts by two other fences. find the maximum area that can be enclosed and separated in this way with 1200m of fencing.
  9. 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 …
  10. area and perimeter

    a farmer wishes to build a fence around a rectangular field and divide it into two equal parts as well.the dividing fence must be parallel to one of the side of the field. you are asked to find dimension of the field of maximum area …

More Similar Questions