# Math Help - Optimization Problem

1. ## Optimization Problem

A farmer has 160 ft of fencing to enclose 2 adjacent rectangular pig pens. What dimensions should be used so that the enclosed area will be a maximum? (give the answer as the dimensions of 1 of the pens)

First I drew the two rectangles and I knew that I had to maximize the area.

Then I got stuck. Thanks for any help!

2. Originally Posted by liz155
A farmer has 160 ft of fencing to enclose 2 adjacent rectangular pig pens. What dimensions should be used so that the enclosed area will be a maximum? (give the answer as the dimensions of 1 of the pens)

First I drew the two rectangles and I knew that I had to maximize the area.

Then I got stuck. Thanks for any help!
we have the condition that 4x + 4y = 160

we also know that the area of one pen is A = xy

now use the condition to write A in terms of one variable, and then maximize A (find it's derivative, set it equal to zero, solve for one variable, then solve for the other using that variable)

3. Thanks so much! I think I can get it from here.

Thanks!!!!

4. Originally Posted by liz155
Thanks so much! I think I can get it from here.

Thanks!!!!
ok, good. tell me if you have any problems. you have the answer in your book right?

5. It's multiple choice. Thanks again.