Optimization of an objective function with probabilistic multipliers.

[avvicena]

I have a main equation i want to find optimum (minimum of Z, solving for y1 and y2) value for:



Given the following constraints:


So, is there a solution for minimum value for Z, using Lagrange multipliers e.g.?

 

[Deleted member 4993]

I have a main equation i want to find optimum (minimum of Z, solving for y1 and y2) value for:

View attachment 20412
Given the following constraints:
View attachment 20414
So, is there a solution for minimum value for Z, using Lagrange multipliers e.g.?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520​

Please share your work/thoughts about this assignment.

 

[avvicena]

i know how to solve the optimization of the variant of this equation with constant values instead of probabilistic of x1, x2 and x3 using Lagrange multipliers:
H = Z(y1,y2) - λ ((2+6x1)/y1 + 6x2/y2 -18)

but when x1, x2, and x3 are probabilistic values (in this case uniform distributions) i dont know how to tackle this problem.