Posted by **Greg** on Thursday, May 1, 2008 at 11:07pm.

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 to enclose the greatest area?

a) Find at least five ordered pairs, comparing pasture length to its area. Remember: only 1000 yards of fencing available.

(Don't i need the maximum to determine this?)

b) Plot your five data points (length and area) on a grid with scales, and join them roughly. You should get the shape of a parabola.

c) Use your graping calculator to find the quadratic function that related to the data.

d) Graph resulting function by hand. State coordinateds of the point of the graps that yields max area. Find max area the farmer can fence in. What are the dimensions?

Can someone help me with this. I am so lost.

All Help is appreciated.

- Applied Math- Gr.11 -
**tchrwill**, Friday, May 2, 2008 at 1:35pm
Considering all rectangles with a given perimeter, one side being provided by a straight given boundry, which one encloses the largest area?

Letting P equal the given perimeter and "x" the short side of the rectangle, we can write for the area A = x(P - 2x) = Px - 2x^2.

Taking the first derivitive and setting equal to zero, dA/dx = P - 4x = 0, x becomes P/4.

With x = P/4, we end up with a rectangle with side ratio of 2:1.

.....The short side is P/4.The traditional calculus approach would be as follows.

.....The long side is (P - 2(P/4)) = P/2.

Therefore, it can be unequivicably stated that of all possible rectangles with a given perimeter, one side being a given external boundry, the rectangle with side ratio of 2:1 encloses the maximum area.

The prime factorization os 1000 is 2^3(5^3).

Therefore, the total number of factors(divisors) is F = (3 + 1)(3 + 1) = 16, namely 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 10, 125, 250, 500 and 1000 enabling 8 possible sets of dimensions.

## Answer this Question

## Related Questions

- word problem - a farmer has 800 yards of fencing to enclose a rectangular ...
- math - a farmer has 200 yards of fencing to enclose three sides of a rectangular...
- Math - A farmer plans to enclose a rectangular pasture adjacent to a river. (see...
- Math - A farmer needs to enclose three sides of a pasture with a fence (the ...
- math - A pasture has four straight sides. Three sides are 3/8 miles long. It ...
- Math - farmer wants to enclose his pasture which is bordered by a river. If he ...
- Math - A farmer with 8000 meters of fencing wants to enclose a rectangular plot ...
- Algebra - Math - A farmer has 100 yards of fencing with which to enclose two ...
- math - A farmer plans to enclose a rectangular region, using part of his barn ...
- Math - a farmer wants to put a fence around a rectangular field and then divide ...

More Related Questions