# applied max/min problems!

• Dec 6th 2009, 01:11 AM
calculusisnotfun
applied max/min problems!
Hi Im new here lol! It's really late and i was working on some calculus. I stumbled across a difficult problem and google led me here. Anyways here is the problem:
A field has boundary a right triangle with hypotenuse along a straight stream. A fence bounds the other two sides of the field. Find the dimensions of the field with maximum area that can be enclosed using 1000 ft of fence.

any pointers? help? THANKS IN ADVANCE
• Dec 6th 2009, 03:29 AM
alexmahone
Quote:

Originally Posted by calculusisnotfun
Hi Im new here lol! It's really late and i was working on some calculus. I stumbled across a difficult problem and google led me here. Anyways here is the problem:
A field has boundary a right triangle with hypotenuse along a straight stream. A fence bounds the other two sides of the field. Find the dimensions of the field with maximum area that can be enclosed using 1000 ft of fence.

any pointers? help? THANKS IN ADVANCE

Let the length of one of the fenced sides of the field be x.
Then the length of the other (fenced) side of the field will be 1000-x.

$\displaystyle A=\frac{1}{2}bh$

= $\displaystyle \frac{1}{2}x(1000-x)$

$\displaystyle \frac{dA}{dx}=\frac{1}{2}(1000-2x)$

= $\displaystyle 500-x$

For maximum area,

$\displaystyle \frac{dA}{dx}=0$

$\displaystyle 500-x=0$

$\displaystyle x=500 m$

$\displaystyle 1000-x=1000-500=500 m$