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The problem provides the profit function for the Bluebird Bakery, given by:

\[
f(x) = -500(x - 0.45)^2 + 400
\]

This function models the profit in dollars, $ f(x) $, where $ x $ represents the price of a cookie in dollars. We are asked to find the profit for two specific cookie prices: $0.40 and $0.75.

### Step 1: Calculate the profit for selling cookies at $0.40 each

Substitute $ x = 0.40 $ into the profit function:

\[
f(0.40) = -500(0.40 - 0.45)^2 + 400
\]
\[
f(0.40) = -500(-0.05)^2 + 400
\]
\[
f(0.40) = -500(0.0025) + 400
\]
\[
f(0.40) = -1.25 + 400 = 398.75
\]

### Step 2: Calculate the profit for selling cookies at $0.75 each

Substitute $ x = 0.75 $ into the profit function:

\[
f(0.75) = -500(0.75 - 0.45)^2 + 400
\]
\[
f(0.75) = -500(0.30)^2 + 400
\]
\[
f(0.75) = -500(0.09) + 400
\]
\[
f(0.75) = -45 + 400 = 355
\]

### Final Answers:
- The profit for selling cookies for $0.40 each is **$398.75**.
- The profit for selling cookies for $0.75 each is **$355.00**.

Would you like more details or have any other questions?

Here are five related questions you might explore:
1. What is the maximum possible profit, and at what price does it occur?
2. How would the profit change if the price of the cookies was increased to $1.00?
3. What is the significance of the constant term 400 in the profit function?
4. How does the negative coefficient $-500$ affect the shape of the profit function?
5. Can you derive a general strategy for maximizing profit in this scenario?

**Tip:** The vertex form of a quadratic function, like the one here, makes it easy to identify the maximum or minimum point, which is useful in optimization problems.

The Bluebird Bakery sells more cookies when it lowers its prices, but this also changes profits. The profit function for the cookies is f(x) = -500(x - 0.45)^2 + 400. This function represents the profit earned when the price of a cookie is x dollars. The bakery wants to maximize its profits. The profit for selling cookies for $0.40 each and $0.75 each needs to be calculated.

Explore how to calculate the profit for selling cookies using a quadratic profit function at Bluebird Bakery. Learn how the price of cookies affects the profits for prices like $0.40 and $0.75, and how to find the maximum profit using algebraic techniques.

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