Question

I have one more word problem that I am stumped on:

A local chicken farmer is constructing a set of eight pens to cage his chickens as shown in the diagram below. He has decided to use 1000 feet of fencing to create the pens.

(I'll attach diagram)

(a) Express the width y as a function of the length x.

y(x)=

(b) Express the total enclosed area A of the pens as function of x.

A(x)=


(c) Determine the dimensions x and y that will maximize the enclosed area.

x=________ feet
y=________ feet

Answer 1

Oh they give you a diagram and everything. How nice.

Answer 2

yeah haha but I still can't figure it out.. wbu?

Answer 3

I'm sure I could figure it out...I'm lazy though

Answer 4

I'll do a). The enclosure will require 5y + 3x of wire, or 5y+3x=1000
Isolating y term: 5y=1000-3x, or y=200-(3/5)x

Answer 5

how do I find (b) & (c)

Answer 6

nvm I figured b out but not c

Answer 7

nvm i figured that out too (: thanks!

Answer 8

Solve for area A. Substitutihg for y, getting
A=x(200-3/5x) or A=200x - (3/5)x^2 differentiate dA/dx getting:
A'=(-3/5) 2x + 200 set to 0 and solve getting x=1000/6 ft
y=100 ft.

so b) A=(-3/5)x^2+200
and
c) x=1000/6 ft., y=100 ft.

Answer 9

Good luck with it, seems you're getting the hang of it.