Question

PLEASE HELP ASAP!!!! FULL ANSWERS ONLY!!!!

Blake 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 Blake has 950 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 a function for the area A of the enclosure in terms of w . (HINT: First write one equation with w and l and one equation with w and l and A. Solve for l in the first equation and substitute for l in the other). A ( w ) = ____________

b) What width w would maximize the area? w = __________________ ft

c) What is the maximum area? A = ______________ square feet

Answer 1

(a) A(w) = w(950-2w) = 950w-2w^2

(b) w = 237.5

(c) A = 112812.5

Explanation:

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

950/4 = 237.5

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

237.5+237.5=475 feet is the length and 237.5 feet is the width(s)

A=475*237.5

A=112812.5 square feet

Doing the algebra...

P=l+2w

950=l+2w

950-2w=l

A=lw

A=(950-2w)w

A=950w-2w^2