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
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
Lagrange multiplier problems typically give something like $\displaystyle f(x,y,z)= \lambda g(x,y,z)$, $\displaystyle h(x,y,z)= \lambda k(x,y,z)$, etc. I have found that it is often best to divide one equation by another, immediately eliminating $\displaystyle \lambda$ (which is not part of the solution, any way).
Here, you have $\displaystyle 40\pi(7r+ \pi)= 2\lambda r h$ and $\displaystyle 80\pi r= \lambda \pi r^2$
Dividing the first equation by the second,
$\displaystyle \frac{7r+ \pi}{2r}= \frac{2h}{r}$
so that $\displaystyle 7r+ \pi= 4h$.
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.)