TITLE: How do I interpret this mathematical model?
QUESTION [1 upvotes]: "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.

REPLY [0 votes]: Costs:
$$C=500000+80x+0.03x^2$$
Income:
$$I=200x$$
Profit/Revenue:
$$R=I-C=200x-(500000+80x+0.03x^2)=-0.03x^2+120x-500000$$
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