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...

Question

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&#039;m not sure.. beacause exist regions where one plan is under the other and only one of them is a minimun...

humbast2 · Accepted Answer

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  =  tsubject to  a  x  +  y  ≥  t    b  y  +  x  ≥  t        p    1    x  +      p    2    y  =  m

Brunton39 · Accepted Answer

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.