(adsbygoogle = window.adsbygoogle || []).push({}); 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 of perimeter ≤ f+40, 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

b.

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

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

c.

P=> 2x+y=160 => y=160-2x

A=> xy=160x-2x^2

3. The attempt at a solution

I worked through the problem and found

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

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

c. x=40, y=80 => A=3200 sq ft

I was just wondering if there was a way I could check these answers?

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# Maximizing area word problem

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