Help with complex systems of equations

**DanielLiwicki** · September 20th 2011, 08:48 PM

Hi All
These equations are the resulte from a lagrange multiplier optimization problem. I can not get the algebra right! Please help!

280*pi*r + 80*pi*hi - 2*lamda*r*h = 0
80*pi*r - lamda*pi*r^2=0
-pi*r^2*h + 100=0

**CaptainBlack** · September 20th 2011, 09:30 PM

Originally Posted by DanielLiwicki

Hi All
These equations are the resulte from a lagrange multiplier optimization problem. I can not get the algebra right! Please help!

280*pi*r + 80*pi*hi - 2*lamda*r*h = 0
80*pi*r - lamda*pi*r^2=0
-pi*r^2*h + 100=0

What is hi?

CB

**DanielLiwicki** · September 20th 2011, 09:32 PM

pi not hi ....sorry

**HallsofIvy** · September 21st 2011, 06:37 AM

Lagrange multiplier problems typically give something like $f(x,y,z)= \lambda g(x,y,z)$ , $h(x,y,z)= \lambda k(x,y,z)$ , etc. I have found that it is often best to divide one equation by another, immediately eliminating $\lambda$ (which is not part of the solution, any way).

Here, you have $40\pi(7r+ \pi)= 2\lambda r h$ and $80\pi r= \lambda \pi r^2$
Dividing the first equation by the second,
$\frac{7r+ \pi}{2r}= \frac{2h}{r}$
so that $7r+ \pi= 4h$ .

You can solve that for either r or h in terms of the other and put into the final equation.

(Are you sure about the "hi= pi"? It seems strange that you would write "pi*pi" rather than "pi^2" and also strange that "pi^2" would show up in such a problem.)

**DanielLiwicki** · September 21st 2011, 06:58 AM

Your Right!!! Not hi...not pi... but just h.

**HallsofIvy** · September 21st 2011, 07:21 AM

So you have 7r+ h= 4h.

**DanielLiwicki** · September 21st 2011, 07:56 AM

It worked out! Thank you!

Thread: Help with complex systems of equations

LinkBack

Thread Tools

Display

Help with complex systems of equations

Re: Help with complex systems of equations

Re: Help with complex systems of equations

Re: Help with complex systems of equations

Re: Help with complex systems of equations

Re: Help with complex systems of equations

Re: Help with complex systems of equations

Similar Math Help Forum Discussions

Solving Linear Equations, Systems of Equations, and Functions.

Real and Complex number systems

Real and Complex Number Systems

Complex base numeral systems?

Systems of Equations

Search Tags