Example
The price for lemonade $$P = 10 - 2 Q$$ Zoe is the only lemonade seller on her street. She controls the quantity of lemonade available on the market.
Her revenue is $$R \left( Q \right) = PQ = \left( 10 - 2Q \right) Q = 10 Q - 2 Q^2$$ If Zoe produces Q=2 liters of lemonade, her revenue is equal to $12: $$R \left( 2 \right) = 10 \times 2 - 2 \times 2^2 = 20 - 8 = 12$$
Question
The price for lemonade follows $$P = 94 - 4 Q$$ What is Zoe's revenue function? What is her revenue if she produces 4 liters of lemonade?
Zoe's revenue function is \begin{align*} R \left( Q \right) &= P Q \\ &= \left( 94 - 4 Q \right) Q \\ &= 94 Q -4 Q^2 \end{align*}
If `Q=8`, then her revenue is \begin{align*} R \left( 8 \right) &= 94 \times 8 - 4 \times 8^2 \\ &= 752 - 256 \\ &= 496 \end{align*}