Differential Calculus Application

[kurimaw]

Just a question regarding Differential Calculus Application. Can anyone help me to solve this using differential calculus. Here it is:

A farmer has enough money to build only 100 meters of fence. What are the dimensions of the field he can enclose the maximum area?

thanks in advanced:D

 

[arildno]

Have you done calculus of variations yet?

 

[HallsofIvy]

Calculus of variations would be needed if you assume the field can be of any shape (a circle give maximum area for a given perimeter). You may be allowed to assume the field is a rectangle. In that case, letting x and y be the length and width, you know that 2x+ 2y= 100 and that the area is A= xy. Solve 2x+ 2y= 100 for either x and y and put that into A= xy to get the function in a single variable. Do you know what to do from there?

(The answer is pretty obvious anyway!).

 

[arildno]

(The answer is pretty obvious anyway!).

At least as long as the ground is flat...

 

[mathwonk]

it depends who owns the land, and what shape his own land has. our friend used the method described and the fence wound up on someone else's land!

 

[bassplayer142]

This is an optimization problem. Use derivatives to find it. It was the section where you learned how to find the max and mins of a graph.