It has been determined that the cost of producing x units of a certain item is 8x+720
.  The demand function is given by p=D(x)=41−0.3x
.

Step 1 of 2 :  Find the revenue function.

The revenue function \( R(x) \) is found by multiplying the price per unit \( p(x) \) by the number of units sold \( x \).

The demand function, which gives the price per unit, is \( p = D(x) = 41 - 0.3x \).

Thus, the revenue function is:

\[
R(x) = x \cdot p(x)
\]

Substitute \( p(x) = 41 - 0.3x \) into the equation:

\[
R(x) = x \cdot (41 - 0.3x)
\]

Simplify the expression:

\[
R(x) = 41x - 0.3x^2
\]

So, the revenue function is:

\[
R(x) = 41x - 0.3x^2
\]

Would you like further details or have any questions?

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Here are 5 related questions to explore further:

1. How do we find the profit function using the revenue and cost functions?
2. At what value of \( x \) is the revenue maximized?
3. What is the marginal revenue function for this problem?
4. How do changes in price affect the revenue function?
5. How do you find the break-even point using the cost and revenue functions?

**Tip:** The maximum revenue typically occurs where the derivative of the revenue function equals zero, as this finds the critical points for maximization.

It has been determined that the cost of producing x units of a certain item is 8x+720. The demand function is given by p=D(x)=41−0.3x. Find the revenue function.

Learn how to derive the revenue function R(x) from a given demand function p(x) = 41 - 0.3x. This guide provides a detailed breakdown, suitable for high school students in Grades 10-12, focusing on algebra and quadratic functions.

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