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Let's break down the information provided in the problem:

1. The weekly revenue from selling emeralds at Eduardo's Emerald Emporium is decreasing at a rate of **€700 per €1 increase in price**. This suggests that:

   \[
   \frac{dR}{dp} = -700 \text{ euros per €1 increase in price}
   \]

2. Additionally, the price is decreasing at a rate of **€0.35 per additional emerald sold**, which implies:

   \[
   \frac{dp}{dq} = -0.35 \text{ euros per additional emerald sold}
   \]

To find the **marginal revenue** (rate of change of revenue with respect to quantity sold, \( \frac{dR}{dq} \)), we can use the chain rule:

\[
\frac{dR}{dq} = \frac{dR}{dp} \cdot \frac{dp}{dq}
\]

Substituting the values:

\[
\frac{dR}{dq} = (-700) \cdot (-0.35) = 245 \text{ euros per additional emerald sold}
\]

### Answers for Each Blank and Option:
1. **\( \frac{dR}{dp} = -700 \)**
2. **\( \frac{dp}{dq} = -0.35 \)**

The marginal revenue, \( \frac{dR}{dq} \), is **245 euros per additional emerald sold**.

### Choosing the Option:
The correct option is **“Euros per additional emerald sold”** at a rate of **245**.

Would you like a more detailed explanation, or do you have any questions?

Here are 5 related questions to deepen understanding:
1. How does the chain rule apply in calculating marginal revenue in economics?
2. What does a negative \( \frac{dR}{dp} \) signify in terms of revenue response to price changes?
3. Why does the rate \( \frac{dp}{dq} \) need to be negative for a decrease in price per additional unit sold?
4. How does understanding marginal revenue help in setting optimal prices in real-life scenarios?
5. What would happen to marginal revenue if the rate of price decrease per emerald sold changed?

**Tip:** In economics, understanding the relationship between price, quantity, and revenue helps in analyzing profit maximization strategies.

The weekly revenue in Euros (€) from the sale of emeralds at Eduardo's Emerald Emporium (EEE) is decreasing at a rate of €700 per €1 increase in price, and the price is decreasing at a rate of €0.35 per additional emerald sold. You are given that dR/dp = ?, and dp/dq = ? What is the marginal revenue? (Be sure to state the units of measurement.)

Learn how to calculate the marginal revenue in a real-life scenario with Eduardo's Emerald Emporium. Using differentiation and the chain rule, determine the rate of revenue change with respect to quantity sold. Understand the impact of price and quantity changes on revenue.

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