I have to maximize U ( x , y ) = M i n (...





I have to maximize U ( x , y ) = M i n ( a x + y , b y + x ) s.a p 1 x + p 2 y = m. I try the traditional solution for a leontieff ( a x 1 + y = b y 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...

Answer & Explanation




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:
Maximize  Z = t
subject to
a x + y t b y + x t p 1 x + p 2 y = m



2022-06-28Added 8 answers

It seems if you solve the system of equations [ p 1 x + p 2 y = m ; a x + y = b y + x ] you get exactly the solution.

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