# Thread: maximization problem

1. ## maximization problem

im not sure if this is the right forum to post this, if not please tell me where i should
i have this problem :

to find the ratio x/y for which the expression $x*exp(-x) + y*exp(-x -y)$
is maximaized

can anyone suggest how to do it ?

thanks

2. Find the maximum of

$\varphi (r)=\max \{f(ry,y):y\in\mathbb{R}\}$

3. thanks for the response, but can you please explain more ?
4. The ratio is $r=x/y$. For every fixed $r$ the function on the line $x=ry$ is $g(y)=f(ry,y)$ . For every $r$ you will find a maximun (I hope), this maximum ( denote it by $\varphi(r)$ ) depends on $r$ . Now, find the maximum of $\varphi$ .