A local sneaker company’s profits π each unit of x sneaker sold has been estimated as
π(x)= 〖-x〗^2+300x-9000
a)Find the number of sneaker sold in order for the company to maximize its profit.
b)What is the maximum level of profit can the company achieve?
c)Find the number of sneaker that the company have to sell in order to breakeven.
d)Sketch the graph for the profit function for this company.

Here's the graph for the profit function \(\pi(x) = -x^2 + 300x - 9000\):

- The parabola opens downward.
- The vertex, indicating the maximum profit, is at \( (150, 13500) \).
- The breakeven points are approximately at \( x = 34 \) and \( x = 266 \).

Do you want details or have any questions?

Here are 5 questions you can ask next:
1. How can I find the derivative of a function?
2. What is the significance of the vertex in a quadratic function?
3. Can you explain the quadratic formula in detail?
4. How do you determine if a function is increasing or decreasing?
5. What are some applications of quadratic functions in real life?

Tip: When working with quadratic functions, identifying the vertex and the direction in which the parabola opens can help you understand the function's maximum or minimum values and overall behavior.

Learn how to maximize profit and find the breakeven point using a quadratic function model. Explore the graph of the profit function π(x) = -x^2 + 300x - 9000, understand the significance of the vertex and breakeven points, and apply mathematical concepts to real-world scenarios. Suitable for high school students studying quadratic functions.

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