Maximum pen area: 60m fencing for sheep pen along brick wall

[Jrekz]

A farmer plans to construct a rectangular pen for his sheep. He has 60 m fence to cover three sides with the remaining side being a brick wall. Advise him in using his amount of fence in a way which maximizes the space for his sheep. How should the farmer choose length l and width x from the wall, for this pen to achieve maximum area?


1. Retrieve the (quadratic) function f(x) which describes the area corresponding to x in a mathematical way. Graph this function f(x) for x running from 0 to 30.

2. Find the required width xmax which yields the largest area, and its corresponding length l as well.

3. Calculate this largest possible area up to 1 m2 precise.

 

[stapel]

A farmer plans to construct a rectangular pen for his sheep. He has 60 m fence to cover three sides with the remaining side being a brick wall. Advise him in using his amount of fence in a way which maximizes the space for his sheep. How should the farmer choose length l and width x from the wall, for this pen to achieve maximum area?

1. Retrieve the (quadratic) function f(x) which describes the area corresponding to x in a mathematical way. Graph this function f(x) for x running from 0 to 30.

2. Find the required width xmax which yields the largest area, and its corresponding length l as well.

3. Calculate this largest possible area up to 1 m2 precise.

What have you tried? Where are you stuck?

For instance, you first drew the picture, labelling the width w and the length L of the pen, using a longer line for the one side that is an existing wall (and is presumed to be however long is needed). Then you used this drawing, together with the information about how much fencing is available, to create a perimeter equation in w and L. What equation did you get? (When you provide this, please state which variable you used for the side of the pen that is parallel to the wall, so we can all be drawing the same picture.)

You solved the perimeter equation for one of the variables. Which one? What did you get? You then plugged this into the "area" formula for a rectangle, to get a formula in only one variable. What did you get? You then used whatever method they've given you for finding the max/min point (that is, the vertex). What did you get?

Please be complete. Thank you!