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.