Posted by **GiGi** on Saturday, July 14, 2012 at 12:56pm.

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? -
**Steve**, Saturday, July 14, 2012 at 2:45pm
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.

## Answer This Question

## Related Questions

- Business Calculus - Bill wants to fence in his rectangular garden so his ...
- College Algebra - A rectangular garden next to a building is to be fenced on ...
- Math - My friend has $80 to spend on a fence for her rectangular garden. She ...
- MATH - You would like to construct a 400-square-foot rectangular garden along ...
- calculus - A rectangular fence has to be built from both wood and metal so that ...
- Math - I want to fence in a square vegetable patch. The fencing for the east and...
- math - A museum groundskeeper is creating a semicircular statuary garden with a ...
- fdr - a rectangular fence is constructed that will enclose 100 ft sq of land. ...
- college Algebra - A rectangular fence is to be built along a river using the ...
- Calculus - ABC Daycare wants to build a fence to enclose a rectangular ...

More Related Questions