A pizza shop owner determined the annual profits 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 determine the annual profit when the pizza shop owner sells 350 pizzas, we will substitute \( n = 350 \) into the profit function \( p(n) = 32n - 0.04n^2 \).

First, substitute \( n = 350 \) into the equation:

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

Calculate \( 32(350) \):

\[ 32(350) = 11200 \]

Now calculate \( (350)^2 \):

\[ (350)^2 = 122500 \]

Now calculate \( 0.04(350^2) \):

\[ 0.04(122500) = 4900 \]

Now substitute these values back into the profit equation:

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

Now calculate \( 11200 - 4900 \):

\[ p(350) = 6300 \]

Thus, the annual profit when the pizza shop owner sells 350 pizzas is $6300.