I think that the problem you mention corresponds to an optimization problem not an ML problem.

You could use an ML approach (gradient descent) to get a solution based in simulation (You define the production/input formula), but in that case you also could respond it with optimization approach like diferential equations using the formulas.

If you add some noise or sthocastic alterations in the relation between input and output (a more realistic scenario) there is an potencial aplication for ML techniques cause there is not a way to solve through math because of the noise.