It has been determined that the cost of producing x units of a certain item is 8x+260
.  The demand function is given by p=D(x)=56−0.4x
find the revenue function

To find the revenue function \( R(x) \), we need to multiply the price per unit \( p \) by the number of units \( x \) sold.

Given:
- Demand function (price per unit): \( p = D(x) = 56 - 0.4x \)

The revenue function \( R(x) \) is calculated as:
\[
R(x) = p \times x
\]
Substituting the demand function into the revenue function:
\[
R(x) = (56 - 0.4x) \times x
\]
\[
R(x) = 56x - 0.4x^2
\]

So, the revenue function is:
\[
R(x) = 56x - 0.4x^2
\]

Would you like more details or have any questions about this process?

Here are 8 related questions you might find useful:

1. How can you find the profit function using the cost and revenue functions?
2. What is the break-even point where revenue equals cost?
3. How do you determine the maximum revenue using the revenue function?
4. What is the marginal revenue function derived from the revenue function?
5. How does the demand function affect the revenue and profit functions?
6. Can you find the value of \( x \) that maximizes the revenue function?
7. How do changes in the demand function parameters affect the revenue function?
8. What would happen to the revenue function if the cost function changed?

**Tip:** To find the maximum or minimum values of functions like revenue or profit, you can take the derivative and set it equal to zero, then solve for the critical points.

Learn how to calculate the revenue function from a given demand function. Understand the relationship between price per unit and quantity sold, using the demand function p(x) = 56 - 0.4x. Suitable for advanced high school students and those studying economics.

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