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?

Question

A: 1,470

B:11, 200

C: 11, 186

D: 6,300

Answer 1

To find the annual profit when the pizza shop owner sells 350 pizzas, we need to substitute \( n = 350 \) into the profit function \( p(n) = 32n - 0.04n^2 \).

First, we calculate \( 0.04n^2 \): \[ 0.04 \times 350^2 = 0.04 \times 122500 = 4900 \]

Next, we calculate \( 32n \): \[ 32 \times 350 = 11200 \]

Now we can substitute these values into the profit function: \[ p(350) = 32 \times 350 - 0.04 \times 350^2 \] \[ p(350) = 11200 - 4900 \] \[ p(350) = 6300 \]

Thus, the annual profit if the pizza shop owner sells 350 pizzas is \( \mathbf{6,300} \).

The correct answer is \( \text{D: } 6,300 \).