
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 $\displaystyle x*exp(x) + y*exp(x y)$
is maximaized
can anyone suggest how to do it ?
thanks

Find the maximum of
$\displaystyle \varphi (r)=\max \{f(ry,y):y\in\mathbb{R}\}$

thanks for the response, but can you please explain more ?
i dont understand your answer

The ratio is $\displaystyle r=x/y$. For every fixed $\displaystyle r$ the function on the line $\displaystyle x=ry$ is $\displaystyle g(y)=f(ry,y)$ . For every $\displaystyle r$ you will find a maximun (I hope), this maximum ( denote it by $\displaystyle \varphi(r)$ ) depends on $\displaystyle r$ . Now, find the maximum of $\displaystyle \varphi$ .