Profit The weekly profit P for a widget producer is a function of the number n of widgets sold. The formula is
P=-2 plus 2.9n minus 0.3n exponent 2.

Here P is measured in thousands of dollars, n is measured in thousands of widgets, and the formula is valid up to a level of 7 thousand widgets sold.
a. Make a graph of P versus n.

Here is the graph of the profit \( P \) versus the number of widgets sold \( n \). As you can see, the profit initially increases with the number of widgets sold but eventually declines as the quadratic term dominates.

Would you like more details on how to interpret this graph, or do you have any questions?

Here are some related questions you might consider:
1. What is the maximum profit the company can achieve based on the formula?
2. For how many widgets sold is the profit maximized?
3. What is the breakeven point (where profit equals zero)?
4. How does the quadratic term affect the behavior of the profit curve?
5. What happens to the profit if more than 7,000 widgets are sold?

**Tip**: To find the maximum or minimum of a quadratic function, you can use the vertex formula \( n = -\frac{b}{2a} \), where \( a \) and \( b \) are coefficients from the quadratic equation \( P(n) = an^2 + bn + c \).

Profit: The weekly profit P for a widget producer is a function of the number n of widgets sold. The formula is P = -2 + 2.9n - 0.3n^2. Here P is measured in thousands of dollars, n is measured in thousands of widgets, and the formula is valid up to a level of 7 thousand widgets sold. a. Make a graph of P versus n.

Explore how to graph the quadratic profit function P(n) = -2 + 2.9n - 0.3n^2 for a widget producer, where P is the profit in thousands of dollars and n is the number of widgets sold. Learn how to find the maximum profit, identify the breakeven point, and understand the impact of the quadratic term. Suitable for Grades 9-11.

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