Word problem - Second derivative test, minimum length of fence

• Feb 24th 2014, 08:59 PM
angie427
Word problem - Second derivative test, minimum length of fence
A developer of an apartment/office complex wants to fence in a rectangular parking lot area of 45000 square meters, and divide it into three parts with two parallel fences both parallel to one side of the rectangle. Each part will have a different parking lot for employees, handicapped parking, and tenants. What is the shortest total length of fence that he can use?

The answer must be found with the second derivative test to show that the length is a minimum.
• Feb 25th 2014, 04:38 AM
BobP
Re: Word problem - Second derivative test, minimum length of fence
Make a start at least.
Then we can see where your difficulties lie.
• Feb 25th 2014, 04:46 AM
Prove It
Re: Word problem - Second derivative test, minimum length of fence
Quote:

Originally Posted by angie427
A developer of an apartment/office complex wants to fence in a rectangular parking lot area of 45000 square meters, and divide it into three parts with two parallel fences both parallel to one side of the rectangle. Each part will have a different parking lot for employees, handicapped parking, and tenants. What is the shortest total length of fence that he can use?

The answer must be found with the second derivative test to show that the length is a minimum.

Have you at least started by drawing a diagram?
• Feb 25th 2014, 08:54 AM
hollywood
Re: Word problem - Second derivative test, minimum length of fence
An overall plan for solution: you get to choose the width of the parking lot, so let that be your variable, call it w. Then you calculate the length of fence as a function of w, and set its derivative to zero. Then solve for w.

If you must use the second derivative test to show it's a minimum, then you must. But it is obvious based on the physical situation.

- Hollywood
• Feb 25th 2014, 08:33 PM
angie427
Re: Word problem - Second derivative test, minimum length of fence
Yes I've drawn a diagram. I think I know now what to do from there.