Your monthly profit (in dollars) from selling magazines is given by
P = 2x + 

x
,
where x is the number of magazines you sell in a month. If you are currently selling x = 50 magazines per month, find your profit and your marginal profit. (Round your answers to two decimal places.)
profit	$ 
marginal profit	$ 
 per additional magazine
Interpret your answers.
Your current profit is $ 
 per month, and would increase at a rate of $ 
 per additional magazine sold per month.

The profit function is given by:

\[
P = 2x + \frac{x}{x}
\]

where $ x $ is the number of magazines sold in a month. We need to find the profit and marginal profit when $ x = 50 $.

1. **Calculate Profit, $ P $:**

   Substitute $ x = 50 $ into the profit function:

   \[
   P = 2(50) + \frac{50}{50}
   \]

   Simplify this:

   \[
   P = 100 + 1 = 101
   \]

   So, the profit when selling 50 magazines is **$101.00**.

2. **Calculate Marginal Profit, $ \frac{dP}{dx} $:**

   To find the marginal profit, we need to take the derivative of $ P $ with respect to $ x $.

   The profit function is:
   \[
   P = 2x + \frac{x}{x} = 2x + 1
   \]

   Taking the derivative with respect to $ x $:

   \[
   \frac{dP}{dx} = 2
   \]

   So, the marginal profit is **$2.00** per additional magazine.

### Interpretation

Your current profit is **$101.00** per month, and it would increase at a rate of **$2.00** per additional magazine sold per month.

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Would you like further clarification on any part of this solution? 

Here are some additional questions that might interest you:

1. How would the profit change if you sold 100 magazines per month?
2. What would happen to the profit if the marginal profit rate was not constant?
3. Can we use the marginal profit to predict profits at different sales levels accurately?
4. How would the profit function look if there was a cost per magazine?
5. What would the profit function be if there was an additional fixed cost?

**Tip:** Marginal profit gives an estimate of the profit increase per unit sold, but it only holds within small ranges around the current quantity.

Your monthly profit (in dollars) from selling magazines is given by P = 2x + x/x, where x is the number of magazines you sell in a month. If you are currently selling x = 50 magazines per month, find your profit and your marginal profit. (Round your answers to two decimal places.)

Learn how to calculate monthly profit and marginal profit from magazine sales using the profit function P = 2x + 1. This example demonstrates how to find the profit at a specific sales volume and interpret the rate of profit increase per additional unit sold, suitable for high school students studying algebra and calculus concepts.

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