The profit P, in thousand of dollars, that a manufacturer makes is a function of the number N of items produced in a year, and the formula is as follows.
P = −0.2N2 + 3.6N − 9    Calculate that value.
 thousand dollars


The given profit function is:

\[
P = -0.2N^2 + 3.6N - 9
\]

To calculate the value of the profit \(P\), you need to substitute a specific value for \(N\), which represents the number of items produced in a year.

Could you provide the value of \(N\) so I can calculate \(P\)?

Let me know if you'd like more details or have any questions.

Here are five follow-up questions to expand the topic:

1. What is the maximum profit the manufacturer can achieve?
2. How does the profit change as the number of items produced increases?
3. What does the negative coefficient of \(N^2\) signify in terms of profit behavior?
4. For what values of \(N\) does the manufacturer break even?
5. How would increasing the production cost affect the profit function?

**Tip**: The vertex of a quadratic function gives either the maximum or minimum value depending on the leading coefficient.

The profit P, in thousands of dollars, that a manufacturer makes is a function of the number N of items produced in a year, and the formula is as follows. P = −0.2N^2 + 3.6N − 9. Calculate that value.

Learn how to calculate the profit using the quadratic function P = −0.2N^2 + 3.6N − 9. Explore concepts such as profit maximization, the behavior of quadratic functions, and vertex calculation, suitable for Grades 10-12.

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