Posted by **beckii** on Monday, November 5, 2007 at 6:38pm.

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 -
**tchrwill**, Monday, November 5, 2007 at 7:41pm
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

## Answer this Question

## Related Questions

- shortest fence - this is my last question from applications of derivatives! A ...
- calculus (optimization) - a rectangular study area is to be enclosed by a fence ...
- Math - A rectangular study area is to be enclosed by a fence and divided into ...
- algebra - The length of a rectangular field is 18 m longer than the width. The ...
- precalculus - A rectangular field is to be enclosed by a fence and divided into...
- Grade 11 Math - A rectangular dog run is to be enclosed by a fence and then ...
- area and perimeter - a farmer wishes to build a fence around a rectangular field...
- math - the length of a rectangular field is 18 m longer than the width. the ...
- Calculus 1 - A rectangular field is enclosed by a fence and seperated into two ...
- calculus - A 384 square meter plot of land is to be enclosed by a fence and ...

More Related Questions