a pizza show owner determines 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 can use the given profit function:

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

Substituting \( n = 350 \):

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

Calculating each term:

1. First term: \( 32 \times 350 = 11200 \)
2. Second term: \( 350^2 = 122500 \) and \( 0.04 \times 122500 = 4900 \)

Now substituting these values into the profit function:

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

Calculating:

\[ p(350) = 6300 \]

So, the annual profit if the pizza shop owner sells 350 pizzas is $6,300.

The correct answer is: d $6,300.