To find the marginal revenue function, $MR(q)$, we need to differentiate the revenue function $R(q)$ with respect to $q$.

The revenue function is: $R(q) = -2q^2 + 800q$

Now, take the derivative of $R(q)$ with respect to $q$: $MR(q) = \frac{d}{dq} \left( -2q^2 + 800q \right)$

Step-by-step:

• The derivative of $-2q^2$ is $-4q$ (using the power rule: $\frac{d}{dq} (q^n) = nq^{n-1}$).
• The derivative of $800q$ is $800$ (since the derivative of a linear term $kq$ is just $k$).

So, the marginal revenue function is: $MR(q) = -4q + 800$

This is the simplified expression for the marginal revenue function.

Let me know if you'd like further details or have any questions!

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Here are 5 questions to expand on this topic:

1. What is the significance of the marginal revenue function?
2. How does marginal revenue relate to the demand function?
3. At what quantity $q$ is the marginal revenue equal to zero?
4. How would you find the maximum revenue from this function?
5. Can marginal revenue be negative? What does it mean in this case?

Tip: Marginal revenue helps you determine how much revenue changes with each additional unit produced or sold.