Suppose this same product has a revenue function is given by R(q)=-6q2+600q where q is the number of items sold.

Determine the revenue made from selling 7 items?

Find the marginal revenue function.

MR(q)=R′(q)=

Let's tackle each part of your question:

### 1. **Determine the revenue made from selling 7 items**

The revenue function is given by:

\[
R(q) = -6q^2 + 600q
\]

Substitute \( q = 7 \) into the revenue function to find the revenue from selling 7 items:

\[
R(7) = -6(7)^2 + 600(7)
\]

Now calculate:

\[
R(7) = -6(49) + 600(7)
\]
\[
R(7) = -294 + 4200
\]
\[
R(7) = 3906
\]

Thus, the revenue from selling 7 items is **3906 units** of currency.

---

### 2. **Find the marginal revenue function**

The marginal revenue function \( MR(q) \) is the derivative of the revenue function \( R(q) \) with respect to \( q \). Let's differentiate \( R(q) = -6q^2 + 600q \).

\[
MR(q) = \frac{d}{dq} \left( -6q^2 + 600q \right)
\]

Using the power rule:

\[
MR(q) = -12q + 600
\]

Thus, the marginal revenue function is:

\[
MR(q) = -12q + 600
\]

---

### Summary:
- The revenue made from selling 7 items is **3906 units**.
- The marginal revenue function is \( MR(q) = -12q + 600 \).

Do you want more details or have any further questions?

Here are 5 related questions to explore further:
1. What is the revenue from selling 50 items?
2. At what quantity of items sold does revenue start to decrease?
3. How do you find the maximum revenue using the marginal revenue function?
4. What does the marginal revenue tell you about the change in revenue for each additional item sold?
5. What happens to the marginal revenue as the number of items increases?

**Tip:** The marginal revenue function shows how much additional revenue is generated by selling one more item!

Suppose this same product has a revenue function is given by R(q) = -6q^2 + 600q where q is the number of items sold. Determine the revenue made from selling 7 items? Find the marginal revenue function.

Learn how to calculate the revenue from selling 7 items using the quadratic revenue function R(q) = -6q^2 + 600q and find the marginal revenue function MR(q). This problem covers key algebraic and calculus concepts and is suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation