# How do I interpret this mathematical model?

"A pharmaceutical company firm manufactures a liquid form of penicillin in bulk at a price of £200 per unit. The total production cost £$C$ for $x$ units is:

$$C = 500,000 + 80x + 0.003x^2$$

and the production capacity of the firm is at most 30,000 units in a specified time.

(a) Write down the revenue £$R$ the firm makes by selling $x$ units of penicillin."

I assume the profit made on each unit is 80$x$, but apart from that I'm not sure how I should go about interpreting and answering this. Thanks in advance.

The profit is not $80x$ but the difference between the sales receipts and the production costs.
It seems that the sales receipts for $x$ units are $£200x$ and the cost is $£C$. The revenue is probably meant to be the difference between these two, assuming all items produced are sold. You are probably expected to state this as a function of $x$.
Revenue is how much you make, full stop, ignoring the costs of production. So in this case, look at how much the company makes by selling $x$ units of penicillin.
Costs: $$C=500000+80x+0.03x^2$$ Income: $$I=200x$$ Profit/Revenue: $$R=I-C=200x-(500000+80x+0.03x^2)=-0.03x^2+120x-500000$$