hawatajwizp

Answered

2022-06-26

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

Answer & Explanation

humbast2

Expert

2022-06-27Added 21 answers

I do not think an analytical solution exists for the problem.
For a numerical solution, you can use the simplex algorithm to solve the problem, once you have linearized it as follows:

subject to
$ax+y\ge t\phantom{\rule{0ex}{0ex}}by+x\ge t\phantom{\rule{0ex}{0ex}}{p}_{1}x+{p}_{2}y=m$

Brunton39

Expert

2022-06-28Added 8 answers

It seems if you solve the system of equations $\left[p1x+p2y=m;ax+y=by+x\right]$ you get exactly the solution.

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