A pizza shop owner determined the annual profit in dollars from selling pizzas using p(n) - 32n 0.04n^2 where n is the number of pizzas sold.What is the annual profit if the pizza shop owner sells 350 pizzas?

Answer 1

To find the annual profit \( p(n) \) when the pizza shop owner sells \( n = 350 \) pizzas, we can use the provided profit function:

\[ p(n) = 32n - 0.04n^2 \]

Substituting \( n = 350 \) into the equation:

\[ p(350) = 32(350) - 0.04(350)^2 \]

Calculating each term:

1. Calculate \( 32(350) \): \[ 32 \times 350 = 11200 \]

2. Calculate \( 0.04(350)^2 \): \[ 350^2 = 122500 \] \[ 0.04 \times 122500 = 4900 \]

Now, substituting these values back into the profit equation:

\[ p(350) = 11200 - 4900 \]

Subtract:

\[ p(350) = 6300 \]

Thus, the annual profit when selling 350 pizzas is:

\[ \boxed{6300} \text{ dollars} \]