So you need to find an optimum price, so I just thought you had to find a stationary point, i.e. when the differentiation equals 0

But if you differentiate Q you just get -80. So you can't set this to 0, nor can the optimum price be -80. So I thought, ok it must be a bit harder than that.

So the cost per unit 'a' = 300,000 + 20a since there is a fixed cost of 300000 and a variable cost of 20 per unit a

But I just don't know where to go from here since cost per unit is not necessarily the price per unit, so we can't sub it into the quantity demanded equation. Even if we did, it wouldn't matter because we would still get 0=a number when we differentiate. I think that you have to somehow set up a quadratic in terms of price per unit and then differentiate THAT. But I just don't know how to do it. Any help?

Screenshot of the problem: