Possible max value a cell can generate (given 2 variables)

I'm likely missing something, but how is G2 related to F2 and F3? How are F2 and F3 calculated?

Is there a reason you are trying to use Goal Seek? Unless your version has something very different from mine, goal seek cannot find max/min -- it can only find a target value (basically a root finding problem like the other thread).
For more complex problems, you will want to use Solver https://support.office.com/en-us/art...B-F63E45925040 In your spreadsheet, I:

1) Called solver and told it to:
2) Set Target cell: G2
3) To a maximum
4) By changing: F2:F3

then clicked Solve to execute. It came back with a quick message that it had found a solution. I noted the values, then entered 20 in F2 and 50 in F3 and repeated the Solver command and it converged on the same maximum. As near as I can tell, Solver readily finds a solution. You have some "discontinuous" functions (IF(), MAX(), MIN()) inside of your calculation sequence, so it may be important to give Solver some good starting values so that it can find the maximum away from those "breaks" in the function. As near as I can tell, though, Solver can find a maximum for this problem.

yes, it can be automated. In the other thread, you noted that you did not have the mathematical literacy to tackle Newton's method in 2 dimensions. I expect one could apply some multivariable calculus to this problem and get the solution, but I doubt we have the mathematical literacy to tackle the problem that way. Therefore, I expect that the easiest way to tackle this will be to explore automating Solver. As before, there will be a certain cost/benefit analysis in deciding how much time/effort to put into programming the automation against how much time/effort automation will save in the future.

I rarely require high levels of automation for Solver. Solver is very good about remembering its settings. When I need to repeat a Solver run, I am two clicks away from manually repeating the Solver one: one click to call Solver (Solver remembers the target cell, by changing cell(s), etc. from previous use) and one click to press the Solve button. I rarely need more automation than that.

Solver can be called through a VBA macro. I included a link to an example in my last post on the other thread. In addition, this tutorial contains a lot of information about calling Solver from VBA: https://peltiertech.com/Excel/SolverVBA.html Using these principles, one can reduce the two clicks (or more if Solver parameters need changing) down to one click to call the macro.

If one is familiar with event procedures, one can call the Solver procedure from within a change or calculate event and have Solver run without input from the user. A couple of primers on event procedures:
http://what-when-how.com/excel-vba/a...-in-excel-vba/
http://www.cpearson.com/Excel/Events.aspx

How far down the "automate Solver" rabbit hole do you want to go?

Does it mean that it's a higher level mathematical problem so we cannot just adjust, copy and paste a solution template of an excel like using the Newton's method in the earlier problem, and need to develop another combinations of equations for this particular problem, which is more difficult than automating Solver itself?

I would not say that we cannot do this by some algorithm like Newton's method. Extending Newton's method from 2 dimensions to 3 dimensions is definitely more complex. In the other thread, we noted that we did not have the mathematical literacy to fully understand and implement Newton's method in 2 dimensions. If we did not have that level of literacy, then we certainly do not have the literacy needed to implement something like Newton's method in 3 dimensions. Solver's programmers have already programmed Newton's method (and other algorithms) into the Solver utility.

In short, without the mathematical literacy to program our own version of the algorithm, yes, it is easier to use their implementation.