edit 2: If you are founding an answer would be interesting to you, please upvote this question, because i may use those point in order to start a new bounty.
Edit 3: Can somebody answer?
Edit 4:I have been thinking this about for a month, but generating nothing, can somebody answer this?
edit 3: The 100 point bounty is already end, so following the rules, i have to create a 200 points bounty. If you love this question, please upvote my question and show some support by answering.
This is the easier version of this problem:
problem no. 50: Part a) What is the general method to find all the maximum/minimum of a algebraic equation and a working example for finding the maximum of a algebraic function $f(a,b,c,d,e)$ with 4 constraints?
If there is no finite numbers of method to solve all maximization problems." rigourously and formally?
The function itself can either be a non-linear algebraic function. Each nonlinear algebraic(no linear here) constraints and must use more than one variable and are some inequality (appear more than 1 times) and some equality(appear more than 1 time). Assuming there are no closed form at the end, could you provide the exact infinite sum method?
Appreciate your motivating example in advance!