Take the tour ×  I'm solving the following problem:  $$
\max_\rho \;\; \rho \; \min\left[\left( \frac{bn}{an-bm}
\right)[(a-m)-\rho], \frac{b}{a}[a-(p+\rho)]\right]$$  where all
constants and variables are defined over $\mathbb{R}^+$.  I feel
like there must be a standard way to deal with these kinds of
weird optimization functions? I don't want to solve this
numerically, I need to do comparative statics at some point.
Even if you don't solve this one, any pointers would be super
helpful. Thanks!  share|improve this question add comment  2
Answers  Here's an equivalent formulation of your problem: $$
\begin{aligned} \max_{\rho, t} & \rho t \\ \text{s.t.} & t \leq
\left( \frac{bn}{an-bm} \right) (a-m-\rho), \\ & t \leq
\frac{b}{a} (a-p+\rho), \\ & \rho \geq 0. \end{aligned} $$ This
is a quadratic program. You can use the KKT conditions to find a
solution.  share|improve this answer Doesn't the $\rho t$
objective make your formulation nonlinear? Still, the KKT
conditions should be linear. –  Mike Spivey Dec 7