Which Kind of Machine Learning should I use for an Optimization Problem?
You have no existing data where the parameters you mentioned have been tweaked and you then have the resulting profits?

If you don't have any pre-labeled data then you will find it very difficult because the NN will have nothing to learn from.  NNs learn from either the information you give; the inputs and corresponding outputs, or by experimenting with values and then using the result of using those outputs as labels / targets to learn from.