Question

Nick wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Nick has 1000 feet of fencing, you can find the dimensions that maximize the area of the enclosure.a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write an function for the area A of the enclosure in terms of w .

Answer 1

First of all the maximum area is always a square. You can get the answer first to check your work later.

1000/4=250 feet

One side is not needed so add that length to the non-parallel side.

250 + 250=500 feet is the length and 250 feet is the width(s)

A=500*250

A=125000 square feet

Doing the algebra...

P = L +2w

1000 = L+ 2w

100 - 2w = l

Area = Length x Weight

A=(1000-2w)w

A=1000w-2w²

`A=1000w-2w^2`