# Constrained maximization of …

I have to maximize $U(x,y)= Min(ax+y, by+x)$ s.a $p_{1}x +p_{2}y =m$. I try the traditional solution for a leontieff $(ax_{1}+y= by_{1}+x)$ function but I'm not sure.. beacause exist regions where one plan is under the other and only one of them is a minimun...

• So $ax_1$ and $by_1$ are constants ? – callculus May 2 '16 at 16:55
• only $a$ and $b$ – Manuel Alejandro Rodriguez May 2 '16 at 20:09

For a numerical solution, you can use the simplex algorithm to solve the problem, once you have linearized it as follows: $$\mbox{Maximize }\; Z= t$$ subject to $$ax+y\ge t\\ by+x\ge t\\ p_1x+p_2y=m$$