Given the profit function:

$P = 4x + 4x + 10 = 8x + 10$

where $x$ is the number of magazines sold in a month. We need to find the profit and the marginal profit when selling 40 magazines per month.

1. Calculating the Profit:

Substituting $x = 40$ into the profit function:

$P = 8(40) + 10 = 320 + 10 = 330 \text{ dollars}$

2. Calculating the Marginal Profit:

The marginal profit is the derivative of the profit function with respect to $x$. The profit function is:

$P = 8x + 10$

Taking the derivative with respect to $x$:

$P' = \frac{d}{dx}(8x + 10) = 8$

So, the marginal profit is 8 dollars, which is constant and does not depend on $x$.

Summary:

• Profit when selling 40 magazines: $330.00
• Marginal profit: $8.00 per magazine

Would you like any additional details or explanations? Here are some related questions to consider:

1. How would the profit change if the number of magazines sold increases by 10?
2. What is the profit when selling 50 magazines per month?
3. How would a change in the profit function affect the marginal profit?
4. Can you find the breakeven point where the profit is zero?
5. What happens to the profit if fixed costs are increased by $20?

Tip: Understanding marginal profit helps in determining how additional sales affect your overall profit, which is essential for making strategic business decisions.