Find the right balance between price of a property and agent fee

I would like to know when buying a property when is better for an estate agent to get a higher fee from me compared to the seller if we get a deal with a lower amount.

As an example, let's say that:

• the property asking price is €350k
• the agent fee for the buyer is 3%
• the agent fee for the seller is 3%

All of the above could be parameters.

I would like e.g. to offer €300k (50k less than the asking price) and e.g. offer the agent a fee of 4%. OK now I could do the calculations and discover if the agent is better off, but I would like to explore the ranges of possible solutions.

Is there a way to know the valid price ranges given an amount for the fee so I know how to bargain the price?

I think this is an optimization problem that could be solved with linear programming. However, I am a bit rusty with maths, vectors and matrices, since I left university a long ago.

Ideally I would like to write a Python script to solve this, or a Jupyter notebook to tune the input parameters.

Perhaps plot a result with the price-ranges, fee thresholds and so on.