Extreme Value Problem

[Timothy133]

Hello guys,
I am currently trying to solve this problem, a woman wants to have 2 fields for plants. One of them is circular and one of them squared. The scope of them both combined is 10 -> so 10 = 2*Pi*r + 4*x. This is the secondary condition. The main one is A= Pi*R² + x². I have to solve the problem for the minimum area possible with the scope of 10.
I am stuck

 

[Dr.Peterson]

I think you are using the word "scope" to mean the length of the boundary. Is that right?

What you need to do is to find an expression for the area as a function of just one variable, which you can do by solving the condition (the "scope" equation) for one variable, either r or x, and putting the resulting equation into the equation for A. Then use whatever technique you have learned to find the minimum. (But why would anyone want the minimum area?? I'd expect to want the maximum!)

 

[Steven G]

scope? Very strange.
Please note that r and R are two different variables. I suspect that you only wanted one of them, so please choose one.
I too suspect that you want to maximize the area so please check the problem.

You did good initial work. Getting to this position is very common in max/min problems. So please remember the instructions from Dr Peterson's post on how to proceed from here.

 

[Dr.Peterson]

I too suspect that you want to maximize the area so please check the problem.

Actually, I don't think the goal is to maximize the area; it turns out that the minimum is more mathematically interesting, as the maximum is just one field. It just doesn't seem very realistic. But then, no units are given, so it isn't real anyway.