Initial Guess Using Scipy.optimize In Python

I have the following problem to code using python: I have 7 parameters: x, y, z, t, HF, M1F, and M2F. The user should input any of these 3 and the program should calculate the rest

Solution 1:

I'm not sure optimization is the right way to go here. I think personally I'd start with the three variables given and algebraically solve the rest. There are a lot of combinations, but all things considered the analytic solution is usually best if it's obtainable.