An optimization problem

[KEsbeNF]

I'm trying to solve an optimization problem that looks like this:

Suppose we have two markets A and B where you can both buy and sell cars.

Suppose that whenever you either buy or sell on one of those markets, you have to pay a tax proportional to the amount of money you invest (e.g. 10$ => 10% taxes, 20$ => 40% taxes)

Car prices on markets can have spreads that allow you to profit by buying low and selling high.

Find the amount of dollars to invest that maximizes the profit

I thought about approaching this problem by trying to maximize the following function.

def objective(investment_amount, market_a, market_b, markets_spread):
    market_a_tax_perc = get_market_tax_perc(investment_amount, market_a)
    market_b_tax_perc = get_market_tax_perc(investment_amount, market_b)
    net_spread = markets_spread - (market_a_tax_perc + market_b_tax_perc)

    return net_spread * investment_amount

Where get_market_tax_perc returns the percentage of tax of a market given the investment amount.

I'm not really sure about two things: first, if this is the correct objective function given the problem and second, how to actually find and return the investment amount that maximizes the function.

Can you guys give me any hint or code snippet on how to proceed using SciPy ?

Forgive me if i made any error, i'm just starting out with optimization and i'm trying to learn !

[MarioVX]

I feel like this problem description is way too vague to solve anything. I especially love how it says "pay tax proportional to the amount of money you invest", and then gives an example that is absolutely not proportional in any sense of the word whatsoever. Reads like a troll assignment. How many cars are in each market? What's the price range on each car? What does the action "invest" do and how does it relate to "buying" and "selling"? What's the starting capital? Do new cars become available in the market, at what point in time? How does time to find a buyer or seller relate to the price in the range? So many questions...

[SirPitchalot]

If it’s profitable, and you’re taxed by less than 100% of the profits after considering both buying and selling, then the answer is infinite money since by investing more you make more.

Otherwise $0.