If fixed costs are $350, what is the profit at the optimal integer output level?

Please specify your answer as an integer.

To find the profit at the optimal integer output level $ q = 5 $, we use the profit function:

\[
\Pi(q) = -4q^2 + 39q - 350
\]

Substitute $ q = 5 $ into the profit function:

\[
\Pi(5) = -4(5)^2 + 39(5) - 350
\]
\[
\Pi(5) = -4(25) + 195 - 350
\]
\[
\Pi(5) = -100 + 195 - 350
\]
\[
\Pi(5) = 95 - 350
\]
\[
\Pi(5) = -255
\]

The profit at the optimal integer output level of 5 units is **-255** dollars.

Do you want more details or have any questions?

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1. What factors can lead to a negative profit even at the optimal output level?
2. How does a negative profit affect business decisions in the short term?
3. What would be the break-even point given the fixed and variable costs?
4. How does the steepness of the marginal cost curve affect profit?
5. What are potential strategies to convert a negative profit into a positive one?
6. How does changing the selling price to $50 per unit affect profit at the same output level?
7. Could reducing fixed costs lead to a positive profit, and by how much?
8. What are the implications of selling fewer units than the optimal output level?

**Tip:** Always check if external factors like changes in market demand could impact your pricing strategy and profitability.

Learn how to calculate profit at the optimal output level using fixed costs of $350 and a quadratic profit function. Step-by-step solution provided. Suitable for undergraduate economics and business students.

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