(adsbygoogle = window.adsbygoogle || []).push({}); PLEASE HELP!! maximizing area problem

1. The problem statement, all variables and given/known data

1. The problem statement, all variables and given/known data

A farmer wants to build a rectangular pen. He has a barn wall 40 feet long, some or all of which must be used for all or part of one side of the pen. In other words, with f feet of of fencing material, he can build a pen with a perimeter of up to f+40 feet, and remember he isn't required to use all 40 feet.

What is the maximum possible area for the pen if:

a. 60 feet of fencing material is available

b.100 feet of fencing material is available

c. 160 feet of fencing material is available

2. Relevant equations

a.

P=> 2x+y=60 => y=60-2x

A=> xy=60x-2x^2

3. The attempt at a solution

I worked through the problem and found

a. For 60 ft of fencing material

x=15, y=30 => A=450 sq ft

I am not sure how to do b and c.

This is my attempt, but I know it is wrong (slightly)

b. For 100 ft of fencing material,

P=> 2x+y=100 => y=100-2x

A=> xy=100x-2x^2

working through this, I end up with

x=25, y=50 => A=1250 sq ft

I know this is wrong because the barn wall is only 40 feet long, and y=50, but all of the 100 feet of fencing has been used up by 2x+y, so there will be 10 feet of fencing missing. How do I rework the problem? Please help i've been working on this for hours!! :(

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# Homework Help: PLEASE HELP maximizing area problem

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