Profit

Example

Zoe is the only lemonade seller on her street. People who drive home stop by to purchase liters of her lemonade.

The demand for lemonade is: $$ P = 10 - 2Q $$

When Zoe produces a quantity `Q` of lemonade, her revenue is $$ R \left( Q \right) = PQ = \left( 10 - 2Q \right) Q $$

Her cost follows the equation $$ C \left( Q \right) = 2 Q $$

Overall, her profit is $$ \Pi \left( Q \right) = R \left( Q \right) - C \left( Q \right) = \left( 10 - 2Q \right) Q - 2 Q = 8Q - 2 Q^2 $$

If Zoe makes 2 liters of lemonade (Q = 2), her profit is $$ \Pi \left( 2 \right) = 8 \times 2 - 2 \times 2^2 = 8 $$

She would make a profit of $8.

Question