# Differential Calculus Application

1. Sep 22, 2007

### 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?

2. Sep 22, 2007

### arildno

Have you done calculus of variations yet?

3. Sep 22, 2007

### 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!).

4. Sep 22, 2007

### arildno

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

5. Sep 22, 2007

### 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!

6. Sep 23, 2007

### 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.